n-n-1-n-2-n-3-n-r-1-

Question Number 41642 by Tawa1 last updated on 10/Aug/18

n (n - 1) (n - 2) (n - 3) \dots . (n - r + 1) = ? ?

Answered by alex041103 last updated on 10/Aug/18

= \frac{n!}{(n - r)!}

Commented by Tawa1 last updated on 10/Aug/18

please workings

Commented by alex041103 last updated on 10/Aug/18

n (n - 1) \dots (n - r + 1) =

= \underset{k = n - r + 1}{\prod^{n}} k = \underset{k = n - r + 1}{\prod^{n}} k \frac{\underset{k = 1}{\prod^{n - r}} k}{\underset{k = 1}{\prod^{n - r}} k} =

= \frac{\underset{k = 1}{\prod^{n}} k}{\underset{k = 1}{\prod^{n - r}} k} = \frac{n!}{(n - r)!}

Commented by Tawa1 last updated on 10/Aug/18

God bless you sir

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