SOLUTION: A committee of 4 people is to be selected from a group consisting of 8 men and 4 women. i. Determine the number of ways in which the committee may be formed if it is to contai

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Question 1185063: A committee of 4 people is to be selected from a group consisting of 8 men
and 4 women.
i. Determine the number of ways in which the committee may be
formed if it is to contain exactly one women.
ii. Find the probability that at least one women is selected onto the
committee
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
i. Determine the number of ways in which the committee may be
formed if it is to contain exactly one women.
Choose the 1 woman any of C(4,1)=4 ways.
Choose the 3 men any of C(8,3)=56

Answer: %284%29%2856%29%22%22=%22%22matrix%281%2C2%2C224%2CWAYS%29

ii. Find the probability that at least one women is selected onto the
committee.
We find the probability that no women (i.e., all men) are chosen, then
subtract from 1.

Number of ways to select all men:  C(8,4)=70 ways
Number of ways to select any 4 people regardless of sex:  C(12,4)=495 ways.

P(all men) = 70/495 = 14/99

P(at least one woman) = 1-14/99 = 99/99-14/99 = 85/99.

Edwin