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Counting Subsets Warmup

Counting Subsets Warmup. We need a committee. … with 3 professors and 2 students. There are 15 professors and 100 students. How many different committees could we form?. But wait!. I forgot to say. Every committee has to have a woman on it. There are 2 women professors and 35 women students.

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Counting Subsets Warmup

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  1. Counting Subsets Warmup

  2. We need a committee … with 3 professors and 2 students. There are 15 professors and 100 students. How many different committees could we form?

  3. But 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.

  4. But wait! I misspoke. There has to be a woman professor AND a woman student. There are 2 women professors and 35 women students.

  5. But 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!

  6. FINIS

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