Question

Va rog frumos
1)sa se arate ca (m+n)! se divide prin m!n!, m,n apartine N*.
2)sa se arate ca (m+n+p)! se divide prin m!n!p!,m,n,p apartine N*.

Answer 1

1)sa se arate ca (m+n)! se divide prin m!n!, m,n apartine N*


$\it \dfrac{(m+n)!}{m!n!} =C^n_{m+n} \in \mathbb{N} \Longrightarrow m!n! | (m+n)!$