Problem:
A box contains five cards, numbered , and . Three cards are selected randomly without replacement from the box. What is the probability that is the largest value selected?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
There are possible equally likely outcomes:
The three highlighted outcomes have as the largest value selected. Hence the probability is .
There are ways to select cards without replacement from a box of cards. If the largest value selected is , then the remaining two cards can be selected from the cards , and in ways. So, the probability that is the largest value selected is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions