Any maths-type people here?
Tachyglossus
different ways that one can select *4 items* from *a collection of 13*.
Anyone wanna walk me through it...?!?
Ta!
T.
Rich Townsend
Well, there's 13 choices for the first item, 12 for the second, 11 for the third
and 10 for the fourth. So the total number of ways is 13*12*11*10.
But, does the order in which the four are selected matter? If not, then we need
to divide by 4! = 4*3*2*1 to account for the fact that we don't care about the
ordering of the selected items.
cheers,
Rich
John Bode
Google "combinatorics".
Combination, no repeats:
n!/r!(n-r)!, where n is 13 and r is 4: 715
Ken Denny
I'm from the US so I'm a math (singular) type person rather than a
maths type person but the way you calculate combinations of n (13)
taking m (4) at a time is n!/(m!*(n-m)!) where ! (factorial) means to
multiply all the integers from that number down to 1 together.
or (13*12*11*10*...*1)/((4*3*2*1)*(9*8*7*6*...*1)) = 715.
Ernest Major
<Tachyg...@ecom.net> writes
>Sorry to be a pest; but I'm wondering how to calculate the number of
>different ways that one can select *4 items* from *a collection of 13*.
If I remember my high-school math it's 13!/(9!*4!) =
(13*12*11*10)/(4*3*2*1) = 13*11*5 = 715.
[ Checks Mathworld (<URL:http://mathworld.wolfram.com/Combination.html>)
- yes that seems to be correct. ]
>
>Anyone wanna walk me through it...?!?
But I don't recall the justification. (A proof by induction would
probably work.)
--
alias Ernest Major
Tachyglossus
news:f1vm7m$hfp$1...@scrotar.nss.udel.edu...
Thanks for this; but I'm afraid it's all looking a bit too complicated for
me!
What I'm wrestling with is a poem of 13 lines, from which someone has to
select 4 lines to be kept, while the remaining 9 lines are deleted. I need
to know how many different ways there are of choosing 4 lines!
Ta!
T.
Peter Pan
Why not selecting 20 from 150?
How many seconds have there been since
the big bang?
jet
I don't think you've been specific enough. For example if the
collection is composed of the integers from 1 to 13 is 1-2-3-4 the
same as 2-1-3-4 or are they different? Do you replace the selected
item before selecting the next so that you could get 1-1-1-1?
Rich Townsend
Well, let me summarize my post:
1) The answer is 13*12*11*10 = 17160 if you care about the ordering of the 4
lines that are chosen.
2) The answer is 13*12*11*10/(4*3*2*1) = 715 if you don't care about the order.
cheers,
Rich
John Brockbank
First of all, try to work out how many ways there are of taking one.
13 of course.
Now, how many ways of taking two? Obviouisly there are 13 ways of
taking the first one. What about the second? Unless you put the
first back, there are 12 ways to choose the second. You can see 11
ways to choose the third, and 10 ways to choose the last. So we have
four numbers, 13 12 11 10. We don't know what to do with them.
Now, suppose we were choosing two from four.
There would be 4 ways of taking the first and three of taking the
second.
The actual ways are:
1 and 2
1 and 3
1 and 4
2 and 3
2 and 4
3 and 4
also
2 and 1
3 and 1
4 and 1
3 and 2
4 and 2
4 and 3
That is 12 ways of doing it. See,. that is 4 times 3. That is the
number of ways of taking the first times the number of ways of taking
the second. So in your example, the numbert of ways of taking four
from 13 is 13 times 12 times 11 times 10.
Notice however that the last 6 are actually the same choices as the
forst 6 only the other way round. If we don't want the second lot, we
have to divide the 4 times 3 by 2. However, since you are talking
about lines in a poem, it makes a heckuva difference doing 1 and 2 or
2 and 1. Remember me, when I am gone away, is different from When I
am gone away, remember me. Poetically anyway.
So your answer is 13*12*11* 10.
Using the asterisk to denote mulitiplication is actually programming
language but will usually be understood unless readers are COBOL
freaks.
See you get maths, poetry, computer programming technique and a bit
of knowledge about COBOL. Aint computers wonderful?
Robert Carnegie
John Brockbank wrote:
However, if the lines are delivered in their order in the original
poem, and not in an order of choosing, then once again it is 13! /
9! / 4! - as has been pointed out, 715. And I lose a little bet with
myself about the distribution of wrong answers in a maths thread,
unless this is the first.
Ye Old One
Not enough for you to evolve a brain.
--
Bob.
Cemtech
peterpa...@gmail.com says...
Peter. Has the bacteria in your skull taken over autonomic functions
yet?
--
Steve "Chris" Price
Associate Professor of Computational Aesthetics
Amish Chair of Electrical Engineering
University of Ediacara "A fine tradition since 530,000,000 BC"
Tachyglossus
> n!/r!(n-r)!, where n is 13 and r is 4: 715
>
Thanks to everyone who took the time to help me out with this!
:-)
T.
Robert Carnegie
can have 13 lines. Aside from that, Amazon UK describes a collection
_101 Very Short Poems_: "The longest poem in this collection is 13
lines and the shortest has no lines at all."
Hmm.
Shall I compare thee to a summer's day?
Rough winds do shake the darling buds of May,
By chance, or nature's changing course untrimmed:
When in eternal lines to time thou grow'st.
I think it's about evolution but I'm not sure :-)
Bill Morse
> We'd like to know more, wouldn't we? Google tells me that a rondeau
> can have 13 lines. Aside from that, Amazon UK describes a collection
> _101 Very Short Poems_: "The longest poem in this collection is 13
> lines and the shortest has no lines at all."
>
> Hmm.
Sounds to me like the title should be _101 Very Short Poems and an Infinite
Number of Very Very Short Poems_
--
Yours, Bill Morse
chris.li...@gmail.com
Do I detect someone who couldn't figure out the answer?
Chris
Robert Carnegie
Bill Morse wrote:
"But Dubiously Similar". yes. Actually I guess the jump is two lines
to no-lines, with "Lines after Dorothy Parker: as follows: Randy is
Dandy" being a zero-linear poem (or my own).
John Wilkins
The latter all covered by a single title: "Ode to Cantor"...
--
John S. Wilkins, Postdoctoral Research Fellow, Biohumanities Project
University of Queensland - Blog: scienceblogs.com/evolvingthoughts
"He used... sarcasm. He knew all the tricks, dramatic irony, metaphor,
bathos, puns, parody, litotes and... satire. He was vicious."
Bill Morse
> Bill Morse <wdNOSP...@verizonOSPAM.net> wrote:
>
>> Robert Carnegie wrote:
>>
>> > We'd like to know more, wouldn't we? Google tells me that a rondeau
>> > can have 13 lines. Aside from that, Amazon UK describes a collection
>> > _101 Very Short Poems_: "The longest poem in this collection is 13
>> > lines and the shortest has no lines at all."
>> >
>> > Hmm.
>> Sounds to me like the title should be _101 Very Short Poems and an
>> Infinite Number of Very Very Short Poems_
>
> The latter all covered by a single title: "Ode to Cantor"...
I had to look that up in my Funk and Wagnalls (well actually wikipedia).
Fortunately by that time I had finished my beer, so my keyboard is still
intact.
--
Yours, Bill Morse
Robert Carnegie
John Wilkins wrote:
> Bill Morse <wdNOSP...@verizonOSPAM.net> wrote:
>
> > Robert Carnegie wrote:
> >
> > > We'd like to know more, wouldn't we? Google tells me that a rondeau
> > > can have 13 lines. Aside from that, Amazon UK describes a collection
> > > _101 Very Short Poems_: "The longest poem in this collection is 13
> > > lines and the shortest has no lines at all."
> > >
> > > Hmm.
> > Sounds to me like the title should be _101 Very Short Poems and an Infinite
> > Number of Very Very Short Poems_
>
> The latter all covered by a single title: "Ode to Cantor"...
"Dante's Eterno, Canto MMMMMMMMMMMMMMXVII"??
But surely there is at most one empty poem, since any other empty poem
has exactly the same words.
And most one-word poems are in the dictionary, except for nonsense
verse, such as Edward Lear's ode, "Pobble", incorporated in a larger
work elsewhere.
- checks that the word "pobble" /is/ not in the dictionary.
John Wilkins
It is a fact everyone knows that empty sets contain an infinite number
of zero-length strings.
Michael Siemon
j.wil...@uq.edu.au (John Wilkins) wrote:
> Robert Carnegie <rja.ca...@excite.com> wrote:
>
> > John Wilkins wrote:
> >
> > > Bill Morse <wdNOSP...@verizonOSPAM.net> wrote:
> > >
> > > > Robert Carnegie wrote:
> > > >
> > > > > We'd like to know more, wouldn't we? Google tells me that a rondeau
> > > > > can have 13 lines. Aside from that, Amazon UK describes a collection
> > > > > _101 Very Short Poems_: "The longest poem in this collection is 13
> > > > > lines and the shortest has no lines at all."
> > > > >
> > > > > Hmm.
> > > > Sounds to me like the title should be _101 Very Short Poems and an
> > > > Infinite Number of Very Very Short Poems_
> > >
> > > The latter all covered by a single title: "Ode to Cantor"...
> >
> > "Dante's Eterno, Canto MMMMMMMMMMMMMMXVII"??
> >
> > But surely there is at most one empty poem, since any other empty poem
> > has exactly the same words.
> >
> > And most one-word poems are in the dictionary, except for nonsense
> > verse, such as Edward Lear's ode, "Pobble", incorporated in a larger
> > work elsewhere.
> >
> > - checks that the word "pobble" /is/ not in the dictionary.
>
> It is a fact everyone knows that empty sets contain an infinite number
> of zero-length strings.
I didn't know that...
John Wilkins
Peter Pan
> John Wilkins wrote:
http://en.wikipedia.org/wiki/Funk_and_Wagnalls
"In 1998, as part of the Information division of Primedia Inc.
(renamed K-III Holdings), Funk & Wagnalls Standard Encyclopedia became
the website funkandwagnalls.com. This short-lived venture was shut
down in 2001. The encyclopedia exists today only as Funk & Wagnalls
New Encyclopedia, an electronic reference provided to educational
institutions by the World Almanac Education Group.
Some content from the encyclopedia became a part of Microsoft's
Encarta digital encyclopedia."
Robert Carnegie
John Wilkins wrote:
Which looked like "Jobsica" at first sight, the 21st century name for
unemployment.
I think in Microsoft SQL Server Transact-SQL - the programming tool
that I use most often - the text string function CHARINDEX(needle,
haystack) returns 0 if needle is an empty string - typically implying
not found - but right now I can't check.
And empty sets don't contain anything. Or, /the/ empty set - there is
only one - doesn't contain anything. The days of the week that begin
with P (in English) and the plays of Shakespeare written after 1700
(by him) and the higher-dimension solutions of the equation in
"Fermat's last theorem" - they are the same thing.
And it's Jobiska. Fish fiddle-dee-dee.
Perplexed in Peoria
"Robert Carnegie" <rja.ca...@excite.com> wrote in message news:1179537074.1...@n59g2000hsh.googlegroups.com...
Named after J.B.S. Haldane's Aunt Jobisca, who was known for her soup.
> Which looked like "Jobsica" at first sight, the 21st century name for
> unemployment.
>
> I think in Microsoft SQL Server Transact-SQL - the programming tool
> that I use most often - the text string function CHARINDEX(needle,
> haystack) returns 0 if needle is an empty string - typically implying
> not found - but right now I can't check.
>
> And empty sets don't contain anything.
Correct.
> Or, /the/ empty set - there is
> only one - doesn't contain anything.
In pure set theory, there is only one empty set. In many versions
of applied set theory, sets are strongly typed. Therefore you have
one empty set for each type. For example, you might have an empty
set of strings, an empty set of integers, or an empty set of persons.
Each of these is a different set, or perhaps better, they are incomparable
sets. But none of them contain an infinite number of zero-length
strings. In fact, no set contains an infinite number of zero-length
strings, unless you are considering an infinite number of different
alphabets.
John Wilkins
Which will be me in a few months
>
> I think in Microsoft SQL Server Transact-SQL - the programming tool
> that I use most often - the text string function CHARINDEX(needle,
> haystack) returns 0 if needle is an empty string - typically implying
> not found - but right now I can't check.
>
> And empty sets don't contain anything. Or, /the/ empty set - there is
> only one - doesn't contain anything. The days of the week that begin
> with P (in English) and the plays of Shakespeare written after 1700
> (by him) and the higher-dimension solutions of the equation in
> "Fermat's last theorem" - they are the same thing.
Hence there are an infinite number of named zero length poems, because
you can apply any name you like to the empty set.
>
> And it's Jobiska. Fish fiddle-dee-dee.
I'd call you a pedant, if I weren't occasionally one myself.
Bill Morse
Who said anything about zero-length strings? The original post was about
poems that contained no _lines_. They can still contain points, so one can
easily fit an infinite number of them in a given book :-)
--
Yours, Bill Morse
Robert Carnegie
Perplexed in Peoria wrote:
> "Robert Carnegie" <rja.ca...@excite.com> wrote in message news:1179537074.1...@n59g2000hsh.googlegroups.com...
> >
> > John Wilkins wrote:
> >
> > > It's called the Jobisca theorem.
>
> Named after J.B.S. Haldane's Aunt Jobisca, who was known for her soup.
I think that's just B.S. ;-)
I note http://www.geocities.com/jswortham/haldane.html
Online coverage seems to be 7 Google hits for haldane.jobiska, 8 for
haldane.jobisca.
Either way, a fact the whole world hasn't said much about - online at
least.
> > Or, /the/ empty set - there is
> > only one - doesn't contain anything.
>
> In pure set theory, there is only one empty set. In many versions
> of applied set theory, sets are strongly typed.
Would you call SQL "applied set theory"? ;-) An empty resultset does
come with metadata that would apply to the data rows if there were any
data rows.
Including column names... if these are limited, as I expect they may
be in formal SQL specifications, in length or in numbe or in
alphabetr, then you may not be able to achieve the infinite strings we
were talking about.
Robert Carnegie
> Robert Carnegie <rja.ca...@excite.com> wrote:
>
> > John Wilkins wrote:
> >
> > > It's called the Jobisca theorem.
> >
> > Which looked like "Jobsica" at first sight, the 21st century name for
> > unemployment.
>
> Which will be me in a few months
I wish I could say I'm sorry.
Well, in fact I can and have said "I'm sorry", it's just that you
couldn't possibly hear it. And this expression of sympathy should not
be taken as a considered opinion that you didn't deserve it, I have no
idea, I'm just being polite... but not very ;-)
> > And empty sets don't contain anything. Or, /the/ empty set - there is
> > only one - doesn't contain anything. The days of the week that begin
> > with P (in English) and the plays of Shakespeare written after 1700
> > (by him) and the higher-dimension solutions of the equation in
> > "Fermat's last theorem" - they are the same thing.
>
> Hence there are an infinite number of named zero length poems, because
> you can apply any name you like to the empty set.
Ah, but if you change the name of a story, is it the same story? If
you change the name of a picture, is it the same picture? (In
abstract art that's the main informational content.) Lewis Carroll
comes in here - "A-Sitting on a Gate", you know.
I suppose that an abstract picture with an obscene title is obscene,
whereas with an innocuous title no one would mind. So it's changed...
> > And it's Jobiska. Fish fiddle-dee-dee.
>
> I'd call you a pedant, if I weren't occasionally one myself.
Mostly I wanted to say "Fish fiddle-dee-dee". Well, as discussed, I
can't. Well, I have... etc. ;-)
Robert Carnegie
Bill Morse wrote:
But a point has no dimension so you can't see 'em without the
lines! ;-)
I presume they meant a poem with one line and therefore no line
breaks, but I haven't investigated, this way is more fun!
Walter Bushell
j.wil...@uq.edu.au (John Wilkins) wrote:
> Hence there are an infinite number of named zero length poems, because
> you can apply any name you like to the empty set.
Giving a thing a different name does not make it another object. Hence
all zero length poems are the same and there is only one.
Mark Isaak
But a potentially infinite number of negative length poems. Probably
many written by the same author who wrote:
First, let me tell you I'm cursed.
I'm a poet whose time gets reversed.
Reversed gets time
Whose poet a I'm.
Cursed I'm you tell me let, first.
--
Mark Isaak eciton (at) earthlink (dot) net
"Voice or no voice, the people can always be brought to the bidding of
the leaders. That is easy. All you have to do is tell them they are
being attacked, and denounce the pacifists for lack of patriotism and
exposing the country to danger." -- Hermann Goering