Question 867360: A task force studying sex discrimination wishes to establish a subcommittee. If the subcommittee is to consist of 11 members chosen at random from a group of 15 men and 18 women, find the probability that the subcommittee consists of the following?
(a) 8 men and 3 women (Round your answer to two decimal places.)
(b) all women (Round your answer to seven decimal places.)
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! There are 15+18 = 33 people total. So there are 33 C 11 = 193,536,720 ways to form a committee of 11 people (with no restrictions on gender).
I'm using the combination formula to compute 33 C 11. It's faster to do with a calculator, but I recommend you do a few by hand to get an idea of how it works.
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a)
There are 15 C 8 = 6,435 ways to pick 8 men (from a pool of 15 men)
There are 18 C 3 = 816 ways to pick 3 women (from a pool of 18 women)
There are 6,435*816 = 5,250,960 ways to pick a committee of 11 people where there are 8 men and 3 women.
Divide this by the total number of ways to form an 11 member committee: 5,250,960/193,536,720 = 0.02713159549258
Then round to two decimal places: 0.02713159549258 ----> 0.03
So the probability of selecting exactly 8 men and 3 women is 0.03
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b)
There are 18 C 11 = 31,824 ways to pick a committee of all women.
Divide this by the total number of ways to form an 11 member committee: 31,824/193,536,720 = 0.00016443391208
Then round to seven decimal places: 0.00016443391208 ----> 0.0001644
So the probability of selecting all women, ie a committee of 11 women, is 0.0001644
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