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Multiplying Terms with the Same Base

If nP100 = ...

Question

If $^{n} P_{100} =^{n} P_{99}$ , then $n$ is equal to

100

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101

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99

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86

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Solution

The correct option is A $100$
Given $^{n} P_{100} =^{n} P_{99}$

Formula: $^{n} p_{r} = \frac{n!}{(n - r)!}$

$\Rightarrow \frac{n!}{(n - 100)!} = \frac{n!}{(n - 99)!}$

$\Rightarrow (n - 99)! = (n - 100)!$

$\Rightarrow (n - 99) (n - 100)! = (n - 100)!$

$\Rightarrow n - 99 = 1$

$\Rightarrow n = 100$

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