Transcript 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?
 15   100 
 3    2   2,252,250
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.
 13   65 
 3    2   1, 359, 358
2,252,250  1, 359,258  892,992
But wait!
• I misspoke. There has to be a woman
professor AND a woman student. There
are 2 women professors and 35 women
students.
 2   14   35   99 
 1    2    1    1   630,630
But wait!
• What I really need is to set up 5 committees A, B, C, D,
E with disjoint membership. How many ways?
 15   100   12   98   9   96   6   94   3   92 
 3    2    3    2    3    2    3    2    3    2  
15!100!12! 98! 9! 96! 6! 94! 3! 92!
3!12! 2! 98! 3! 9! 2! 96! 3! 6! 2! 94! 3! 3! 2! 92! 3! 0! 2! 90!
• 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!
FINIS