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Problem 884

AMC 10/12, early questions

Combinatorics Difficulty 4.0 Find the answer Philippine Mathematical Olympiad · Philippines

What is the sum of all four-digit numbers that each use the digits $2, 4, 6$ , and $8$ exactly once?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Official solution

Solution:
Every digit appears in each decimal place exactly $6$ times. Therefore, the sum is $6 \cdot (2+4+6+8) \cdot 1111 = 133,320$ .

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