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HMMT 二月 2009 · 冲刺赛 · 第 13 题

HMMT February 2009 — Guts Round — Problem 13

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 8 ] How many ordered quadruples ( a, b, c, d ) of four distinct numbers chosen from the set { 1 , 2 , 3 , . . . , 9 }
    satisfy b < a , b < c , and d < c ?
解析

英文解析

  1. [ 8 ] How many ordered quadruples ( a, b, c, d ) of four distinct numbers chosen from the set { 1 , 2 , 3 , . . . , 9 }
    satisfy b < a , b < c , and d < c ?
    Answer: 630
    Solution: Given any 4 elements p < q < r < s of { 1 , 2 , . . . , 9 } , there are 5 ways of rearranging
    ( )
    them to satisfy the inequality: prqs , psqr , qspr , qrps , and rspq . This gives a total of · 5 = 6309
    quadruples.4