HMMT 二月 2000 · POW 赛 · 第 6 题
HMMT February 2000 — POW Round — Problem 6
题目详情
英文原题
- Find the number of om binations of length k that use elemen ts from a set of n distin telemen ts, allo wing rep etition.
解析
英文解析
- Sin e we w an t to ho ose k times from n distin t elemen ts, this is equiv alen t to ho osing where to put n 1 "dividers" that separate the hoi es. F or example, if we w an tedto ho ose 3 s o ops of i e ream from the a v ors ho olate, v anilla, stra wb erry , and o ee,
we an represen t the hoi e of 2 v anilla and 1 o ee b y (divider), hoi e, hoi e,(divider),(divider), ho
Noti e that the hoi es of p ositions for the dividers ompletely determines which elemen ts we ho ose. Therefore, we have n + k 1 spa es to ll with n 1 dividers, so then + k 1 n + k 1
number of w a ys of doing this is orn 1 k