Track / Stage 2 / 136 of 240 #376 of 2444

Problem 376

Combinatorics Difficulty 2.6 Multiple choice CEMC Cayley · Canada · 2024

Each of the four digits of the integer $2024$ is even. How many integers between
$1000$ and $9999$ , inclusive, have the property that
all four of their digits are even?

Pick one

Official solution

The integers between $1000$
and $9999$ , inclusive, are all
four-digit positive integers of the form $abcd$ .

We want each of $a$ , $b$ , $c$ , and $d$ to be even.

There are $4$ choices for $a$ , namely 2, 4, 6, 8. ( $a$ cannot equal $0$ .)

There are 5 choices for each of $b$ ,
$c$ and $d$ , namely $0$ , $2$ , $4$ , $6$ , $8$ .

The choice of each digit is independent, and so the total number of such
integers is $4 $\times 5 \times 5 \times$
5 $or$ 500$.

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