If ^nP_4= 360, find the value of n. - Vidyadip

Question

If $^\text{n}\text{P}_4= 360,$ find the value of n.

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Answer

We have,$^\text{n}\text{P}_4= 360,$
$\Rightarrow \frac{\text{n!}}{(\text{n}-4)!}=360$]
$\Rightarrow \frac{\text{n}(\text{n}-1)(\text{n}-2)(\text{n}-3)(\text{n}-4)!=360}{(\text{n}-4)!}$ $\Rightarrow \text{n}(\text{n}-1)(\text{n}-2)(\text{n}-3)=6\times 5\times4\times3 $ $\Rightarrow \text{n}=6 \ [13 \text{ by} \text{ comapring}]$ Hence, $\text{n}=6$

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