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HMMT 二月 2000 · POW 赛 · 第 14 题

HMMT February 2000 — POW Round — Problem 14

专题
Discrete Math / 离散数学
难度
L3
来源
HMMT

题目详情

  1. Find the n um b er of w a ys to distribute sev en distin t balls in to three distin t b o xes if ea h b o x m ust on tain a di eren t n um b er of balls, allo wing an empt y b o x.
解析
  1. The b o xes an b e in an y order, so w e ha v e a fa tor of 6. Sev en an b e partitioned in to h i 7! 7! 7! 7! three distin t parts as 0,1,6; 0,2,5; 0,3,4; or 1,2,4. So, the answ er is 6 + + + = 0!1!6! 0!2!5! 0!3!4! 1!2!4! 1008 .