Question

Find the value of n if nP3 = 120

Answer 1

n= 6
I hope it will help you

Answer 2

Answer:

$\red { Value \:of \:n }\green {= 6 }$

Step-by-step explanation:

$Given \: ^nP_{3} = 120$

$\boxed {\pink { ^nP_{r} = \frac{n!}{(n-r)!} }}$

$\implies \frac{n!}{(n-3)!} = 120$

$\implies \frac{n\times (n-1) \times (n-2)\times (n-3)!}{(n-3)!} = 120$

$\implies n\times (n-1) \times (n-2) = 6\times 5 \times 4$

$\implies n\times (n-1) \times (n-2) = 6\times (6-1) \times (6-2)$

/* Comparing both sides , we get

$n = 6$

Therefore.,

$\red { Value \:of \:n }\green {= 6 }$

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