數學難題一道

2009-12-03 8:18 pm
Let K = abcdefghi
a<b<c<d<e<f<g<h<i
- - - - - - - -
(each symbol represents a "less than or equal to" )

For example, 123456789 or 122223455

How many 9-digit number would satisfy the given condition ?
更新1:

it is a is less than or equal to b is less than or equal to c is less than or equal to d is less than or equal to e is less than or equal to f is less than or equal to g is less than or equal to h is less than or equal to i

回答 (1)

2009-12-04 1:25 am
✔ 最佳答案
本質上這是一道可重組合問題的變相,換個問法,題目等價於 :
『從 1 至 9 中選出 9 個數,允許重複,共有多少種組合?』

可重組合公式 :

從 n 個元素中取 r 個,允許重複,共(n+r-1) C r 種組合。(記為 n H r .)

本題情況 n = 9 , r = 9 , 共 9 H 9 = (9+9-1) C 9 = 24310

共 24310 個九位數符合條件。



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