Track / Stage 4 / 212 of 340 #472 of 2000

Problem 472

AMC 12 late, AIME early

Combinatorics Difficulty 4.9 Find the answer

2、Use $1, 2, 3, 4$ to form a four-digit number $\overline{a b c d}$ , with the following requirements:
（1） $a, b, c, d$ are all different; （2） $b$ is greater than $a$ and $d$ , and $c$ is greater than $a$ and $d$ . How many such four-digit numbers are there? $\qquad$

Your answer

Official solution

【Analysis】From the problem, $b$ and $c$ should take $3$ and $4$ , $a$ and $d$ should take $1$ and $2$ , there are $2 \times 2=4$ numbers

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