PLZ HELP:combinations: what is the result of dividing a 'n' factorial by another m factorial? PLZ HELP ME PLZ

Question

PLZ HELP:combinations: what is the result of dividing a 'n' factorial by another m factorial? PLZ HELP ME PLZ
like in the question in which we have to get identical pairs of a group 3p
answer: 3p!/( (p!)^3*3! )

i would PREFER i logical explanation

i wanna know why we actually divided by 3!..what was the significance?
what does it do: explain WITH LOGIC

Answer 1

In the example you give,
3p!/( (p!)^3*3! ) = 3p!/( (p!)^3*6 ) = 3p!/( (p!)^18) = 3/(p!)^17

In general if n > m,
n!/m! = 2 * 3 * 4 * . . . * m * (m + 1) * (m + 2) + . . . (n - 1) * n / (2 * 3 * 4 * . . . * m) =
(m + 1) * (m + 2) + . . . * (n - 1) * n

Answer 2

yes