Track / Stage 4 / 300 of 340 #560 of 2000

Problem 560

AMC 12 late, AIME early

Combinatorics Difficulty 5.0 Find the answer

$\begin{aligned} & {\left[\begin{array}{l}\text { Rule of product } \\ \text { [Decimal number system }\end{array}\right]}\end{aligned}$

How many six-digit numbers exist, all digits of which have the same parity?

Your answer

Official solution

Note that 0 cannot stand in the first place.

## Answer

$9 \cdot 5^{5}$ numbers.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.