Track / Stage 1 / 93 of 320 #93 of 2604

Problem 93

Combinatorics Difficulty 1.0 Find the answer UKMT Senior Mathematical Challenge · United Kingdom · 2016

Aaron has to choose a three-digit code for his bike lock. The digits can be chosen from 1 to 9. To help him remember them, Aaron chooses three different digits in increasing order, for example 278. How many such codes can be chosen?

(A) $779$ (B) $504$ (C) $168$ (D) $84$ (E) $9$

The source for this one didn't record the answer, so there is nothing to check what you type against. Work it on paper and mark yourself against the solution below.

We don't reproduce this publisher's solutions. Their own solution is here — work the problem first.

Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project. Solutions are the publisher's, linked not copied.