Question

Prove that n(n-1)(n-2)(n-3)_ _ _ _ (n-r+1)= n!/(n-r)!​

Answer 1

Answer:

$since \: \: n! = 1.2.3........ \\... (n - r - 1)(n - r)(n - r + 1).... (n - 2)(n - 1)n \\ \\ \implies n ! = (n - r)! \times (n - r + 1).... (n - 2)(n - 1)n \: \: \: \\\ so \: \: \\ \frac{ n!}{(n - r)!} = (n - r + 1)(n - r + 2)......(n - 1)n \\or \\ \frac{ n!}{(n - r)!} =n(n - {1})(n - 2).....(n - r + 2)(n - r + 1)$