If ^n P_4 ;: ; ^n P_5 = 1:2, then n =

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MCQ

If ${}^n{P_4}\;:\;{}^n{P_5} = 1:2$, then $n = $

A
$4$
B
$5$
✓
$6$
D
$7$

✓

Answer

Correct option: C.

$6$

c
(c) $\frac{{n\;!}}{{(n - 4)\;!}} \times \frac{{(n - 5)\;!}}{{n\;!}} = \frac{1}{2}$

$\Rightarrow n - 4 = 2 $

$\Rightarrow n = 6$.

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