Problem:
A bag contains four pieces of paper, each labeled with one of the digits or , with no repeats. Three of these pieces are drawn, one at a time without replacement, to construct a three-digit number. What is the probability that the three-digit number is a multiple of
Answer Choices:
A.
B.
C.
D.
E.
Solution:
A number is a multiple of three when the sum of its digits is a multiple of . If the number has three distinct digits drawn from the set , then the sum of the digits will be a multiple of three when the digits are or . That means the number formed is a multiple of three when, after the three draws, the number remaining in the bag is or . The probability of this occurring is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions