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Problem 137

Combinatorics Difficulty 1.4 Multiple choice CEMC Gauss (Grade 7) · Canada · 2015

How many different 3-digit whole numbers can be formed using the digits $4,7$ and $9$ , assuming that no digit can be repeated in a number?

Pick one

Official solution

Using the digits $4,7$ and 9 without repeating any digit in a given number, the following 3-digit whole numbers can be formed: $479, 497, 749, 794, 947,$ and 974.
There are exactly 6 different 3-digit whole numbers that can be formed in the manner described.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.