If $^{n} P_{r} = 840,^{n} C_{r} = 35$ , then $n$ is equal to:

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Solution

The correct option is B 7
$\frac{^{n} P_{r}}{^{n} C_{r}} = r! = \frac{840}{35} = 24 \Rightarrow r = 4$
$^{n} P_{r} = \frac{n!}{(n - r)!} = 840$
$\Rightarrow n \times (n - 1) \times (n - 2) \times (n - 3) = 840$
$\Rightarrow 840 = 4 \times 5 \times 6 \times 7$
$\Rightarrow n = 7$

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Similar questions

If $^{n} P_{r}$ = 840, $^{n} C_{r}$ = 35, then n is equal to

^{n} P_{r} = 840,^{n} C_{r} = 35

^{n} P_{r} =^{n} P_{r + 1}

^{n} C_{r} =^{n} C_{r - 1}

r

^{n} P_{r} = 30240

^{n} C_{r} = 252,

(n, r)

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