A committee is to be formed by randomly choosing 4 people from 8 candidates. If Alice and Bob are candidates, what is the probability that Alice will be selected but Bob will not? Select the correct option
A) 1/3
B) 2/5
C) 3/5
D) 1/7
E) 2/7
The total number of ways to form a committee is 8C4=70.   The number of committees which include Alice but not Bob is 6C3=20.   The probability that Alice is selected but Bob is not selected is 20/70=2/7.   The answer is 2/7.
<result>E</result>
A committee is to be formed by randomly choosing 4 people from 8 candidates. If Alice and Bob are candidates, what is the probability that Alice will be selected but Bob will not?