Possible Course Combinations
LOUiS
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School lists 5 periods of Maths: 0800, 0900, 1000, 1300 and 1400;
school lists three periods of Chem, 0800, 1000 and 1300; also 2 periods
of Englishh, 0900 and 1400. A student makes choice of schedule. How
many schedules can be made? Answer of the book is 18. I can find only
15. What is the trick and is there a formula to compute this?
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And here is my answer.
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To find the total number of combinations, you have to multiply 5 math
courses by 3 chemistry courses by 2 english courses = 30.
Some of the classes occur at the same time. So, subtract any
possibilities that overlap.
0800 math and 0800 chemistry, subtract 2 (2 possibilities because of
the english class).
0900 math and 0900 english, subtract 3 (3 possibilities because of the
chemistry class).
1000 math and 1000 chemistry, subtract 2 (2 possibilities because of
the english class).
1300 math and 1300 chemistry, subtract 2 (2 possibilities because of
the english class).
1400 math and 1400 english, subtract 3 (3 possibilities because of the
chemistry class).
So, 30-2-3-2-2-3=18 I hope this answers your question. If you need any
more clearification, do not hesitate to ask.
You can find a detailed answer here:
http://www.thelouisguy.com/files/probmathchemistryenglish.pdf
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