A committee is to be formed by randomly choosing 5 people from 7 candidates. If Alice and Bob are candidates, what is the probability that Alice will be selected but Bob will not?  Choices
A) 3/7  B) 4/7  C) 5/21  D) 6/21  E) 9/42
The total number of ways to form a committee is 7C5=21.   The number of committees which include Alice but not Bob is 5C4=5.   The probability that Alice is selected but Bob is not selected is 5/21.   The answer is 5/21.
<result>C</result>
A committee is to be formed by randomly choosing 5 people from 7 candidates. If Alice and Bob are candidates, what is the probability that Alice will be selected but Bob will not?