Track / Stage 5 / 51 of 400 #651 of 1964

Problem 651

AIME late

Combinatorics Difficulty 5.2 Find the answer

Problem 2

Given the sets: $A=\{0,1,2,3\}$ and $B=\left\{2^{x} \mid x \in A\right\}$

a) Determine the elements of the set $A \cap B$ ;

b) Determine $\operatorname{card} M$ , where $M=\{\overline{a b c} \mid a, b, c \in A$ and $a \neq b \neq c\}$ .

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Official solution

## Problem 2

a) $B=\{1,2,4,8\}$ $2 p$

$A \cap B=\{1,2\}$ $2 p$

b) The digit $a$ can be chosen in 3 ways, the digit $b$ can also be chosen in 3 ways, and the digit $c$ in 2 ways, so there are $3 \cdot 3 \cdot 2$ possibilities. Card $M=18$ $3 p$

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