# The number of ways in which $n$ different things can be distributed into $r$ different groups is coefficient of $x^n$ in $n!(e^x-1)^r$?

This is the question of combination.

I have tried this but how can the binomial expansion can result our need? How we can proof the formula:

The number of ways in which n different things can be distributed into $r$ different groups is coefficient of $x^n$ in $n!(e^x-1)^r$?

• $n!(e^x-1)$ is an expression that is independent of $r$, are you sure you stated the question correctly? math.meta.stackexchange.com/q/5020/306553 also, learn mathjax to type maths on this site. – Siong Thye Goh Sep 6 '17 at 5:32
• @SiongThyeGoh , there's an $r$ in the expression, maybe it has been edited since you originally commented. – TeeJay Sep 6 '17 at 6:33
• Yes...I have edited that..after siong Thye Goh commented – Kazi Abu Rousan Sep 6 '17 at 9:45