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6.Permutation and Combination
easy
If $^{n}{P_4} = 24.{\,^n}{C_5},$ then the value of $n$ is
A
$10$
B
$15$
C
$9$
D
$5$
Solution
(c) Given, $^n{P_4} = 24\,.{\,^n}{C_5}.$
Therefore,$n(n – 1)\,(n – 2)\,(n – 3)$
$ = 24 \times \frac{{n(n – 1)\,(n – 2)\,(n – 3)\,(n – 4)}}{{5.4.3.2.1}}$
$ \Rightarrow $$1 = \frac{{(n – 4)}}{5}$ ==> $n – 4 = 5$ ==> $n = 9$.
Standard 11
Mathematics
