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counting and probability junior

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 ?
(A)
(B)
(C)
(D)
Solution
The number of ways to form a 3-digit number is . The combination of digits that give us multiples of 3 are (1,2,3) and (2,3,4), as the integers in the subsets have a sum which is divisible by 3. The number of 3-digit numbers that contain these numbers is . Therefore, the probability is .
Final answer
C