若c (3上标,n+1下标)-c(3上标,n下标)=15,求C(3,n)

问题描述:

若c (3上标,n+1下标)-c(3上标,n下标)=15,求C(3,n)

(n+1)!/(n-2)!*3!-n!/(n-3)!*3!=15
(n+1)n(n-1)-n(n-1)(n-2)=15*3!
n(n-1)(n+1-n+2)=15*6
n²-n-30=0
n=6
所以原式=6!/3!*3!=20