How do you simplify ((n-k)!) /( n!)(n−k)!n!?

1 Answer
Topscooter
Dec 18, 2015

((n-k)!)/(n!) = 1/((n-k+1)!)(n−k)!n!=1(n−k+1)!

Explanation:

You simply develop n!n! and (n-k)!(n−k)!. n-k < nn−k<n so (n-k)! < n!(n−k)!<n! and (n-k)!(n−k)! divides n!n!.

All the terms of (n-k)!(n−k)! are included in n!n!, hence the answer.

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