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Question Number 74000 by mhmd last updated on 17/Nov/19

i f p_{r}^{n} = 840, c_{r}^{n} = 35 f i n d v a l u e o f r ?

p l e a s s i r h e l p m e ?

Answered by MJS last updated on 17/Nov/19

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

P_{r}^{n} = \frac{n!}{(n - r)!} = C_{r}^{n} \times r!

C_{r}^{n} = 35

P_{r}^{n} = 840

35 r! = 840

r! = 24

r = 4

\Rightarrow

\frac{n!}{(n - 4)!} = 840

n (n - 1) (n - 2) (n - 3) = 840

n^{4} - 6 n^{3} + 11 n^{2} - 6 n - 840 = 0

(n - 7) (n + 4) (n^{2} - 3 n + 30) = 0

n ⩾ 0 \Rightarrow n = 7

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