Counting Subsets Warmup... There are 15 professors and 100 students... But wait!• I forgot to say.. Every committee has to have a woman on it.. There are 2 women professors and 35 women
Trang 1Counting Subsets Warmup
Trang 2We need a committee
• … with 3 professors and 2 students There are 15 professors and 100
students How many different
committees could we form?
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Trang 3But wait!
• I forgot to say Every committee has
to have a woman on it There are 2 women professors and 35 women
students
• OK, remove the committees with no women
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Trang 4But wait!
• I misspoke There has to be a woman professor AND a woman student
There are 2 women professors and
35 women students
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Trang 5But wait!
• What I really need is to set up 5 committees A, B, C,
D, E with disjoint membership How many ways?
• If rearranging the same committees to have
different names is not considered creating a
different set of committees, this number must be
divided by 25!
15
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Trang 6FINIS