simplify n!/(n-2)!2!

Sure, let's simplify the expression step by step:

1. n!/(n-2)!2!

First, let's understand what the factorial (!) means. The factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example, 5! = 54321 = 120.

2. Now, let's expand the factorials in the expression:

n! = n*(n-1)(n-2)(n-3)...321

(n-2)! = (n-2)(n-3)...32*1

2! = 2*1

3. We can see that (n-2)! is a part of n!, so we can simplify the expression by canceling out the common terms:

n!/(n-2)!2! = [n*(n-1)(n-2)(n-3)...321] / [(n-2)(n-3)...3212*1]

After canceling out the common terms, we get:

n!/(n-2)!2! = n*(n-1) / 2*1

4. Finally, we simplify the expression:

n!/(n-2)!2! = n*(n-1)/2

So, the simplified form of the expression n!/(n-2)!2! is n*(n-1)/2.