If 2P(5, 3) $=$ P(n, 4), then $n = 6.$

True

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False

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Either

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Neither

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Solution

The correct option is B False
$2 \times P (5, 3) = P (n, 4) 2 \times {^{5} P}_{3} = {^{n} P}_{4} 2 \times \frac{5!}{2!} = \frac{n!}{(n - 4)!} 2 \times \frac{5 \times 4 \times 3 \times 2 \times 1}{2 \times 1} = n \times (n - 1) \times (n - 2) \times (n - 3) 5! = n! n = 5$
Hence given $n = 6$ is false

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