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6.Permutation and Combination
easy
જો $_n{P_4} = 24.\,\left( {\begin{array}{*{20}{c}}
n \\
5
\end{array}} \right)$ હોય , તો $n= .........$
A
$5$
B
$9$
C
$10$
D
$15$
Solution
$_n{P_4} = 24.\,\left( {\begin{array}{*{20}{c}}
n \\
5
\end{array}} \right)$
$\frac{{n\,!}}{{(n – 4)\,!}} = 24.\,\frac{{n\,!}}{{5\,!\,(n – 5)\,!}}\,\,\,$
$\frac{{n\,!}}{{(n – 4)(n – 5)\,!}} = \,\,24.\,\frac{{n\,!}}{{120\,(n – 5)\,!}}\,\,$
$\,\therefore \,\,\,\,\,\frac{1}{{n – 4}} = \frac{1}{5}\,\,\,\,\,\therefore \,\,\,n – 4 = 5\,\,\,\,\therefore n = 9$
Standard 11
Mathematics
