How does the permutation and combination formula CNM (n is subscript, M is superscript) = n! / m! (n-m)! Come from Please give an example

How does the permutation and combination formula CNM (n is subscript, M is superscript) = n! / m! (n-m)! Come from Please give an example

Cnm=Anm/Amm.
In the formula, the permutation number (also called optional permutation number) and the total permutation number ANN are expressed as follows:
1) The expression of continued multiplication is: anm = n (n-1) (n-2)... (n-m + 1)
2) Factorial expression: anm = n! / (n-m)
Ann=n(n-1)(n-2)...3*2*1=n!
For example: A85 = 8 * 7 * 6 * 5 * 4;
A85=8*7*6*5*4*3*2*1/3*2*1=8!/(8-5)!
Combination number CNM = anm / AMM = n (n-1) (n-2)... (n-m + 1) / M (m-1) (m-2)... * 3 * 2 * 1 [AMM --- total permutation number]
=n!/m!(n-m)!.*2*
For example: C85 = 8 * 7 * 6 * 5 * 4 / 1 * 2 * 3 * 4 * 5 = [8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 / 1 * 2 * 3] / 1 * 2 * 3 * 4 * 5
=8*7*6*5*4/1*2*3*4*5
=56.
Note: the formula of combination number is derived from the expression of permutation number