Re: probability/counting question

[Mike Delanis]

<natema...@gmail.com> wrote in message
news:ef283a82-02a3-4a04...@googlegroups.com...

>Consider a bag containing 8 red balls, 6 green balls, 6 blue balls, and 5
>yellow balls.
>You draw until you get one of the following:
>3-red, 3-green, 4-blue, 4-yellow.

which means draw till you get 3-red, or 3-green, or 4-blue, or 4-yellow

>In all possible games, how many ways are there to get 3 red balls?

all possable games of which subset?



My attempt at a solution:
C(8,3)*(C(6,0)+C(6,1)+C(6,2))*(C(6,0)+C(6,1)+C(6,2)+C(6,3))*(C(5,0)+C(5,1)+C(5,2)+C(5,3))
is the number of strings containg the possilbe colors in all games. Now I
need to work out ordering them, so that it ends on red. What I did is make a
lexographic ordering of 3 red with 0-2 green with 0-3 blue with 0-3 yellow
(48 possibilites). Then I multiplied each outcome length from the
combination formula above time (length - 1) factorial. I think this is
correct, but the numbers are oo big for excel. Does this sound like I am on
the right path?

Thanks!