If $^{2}^{0} P_{r} :^{2}^{0} P_{r}_{-}_{1} = 15 : 1$ , then $r$ $=$

6

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7

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8

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9

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Solution

The correct option is B $6$
$\frac{^{20} P_{r}}{^{20} P_{r - 1}} = \frac{15}{1}$
$[\frac{20!}{(20 - r)!}] / [\frac{20!}{(20 - r + 1)!}] = 15$
$\frac{(21 - r)!}{(20 - r)!} = 15$
$21 - r = 15$
$r = 6$

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