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6.Permutation and Combination
medium
જો $_n{P_4}\, = \,\,720\,\,\left( {\begin{array}{*{20}{c}}
n \\
r
\end{array}} \right)$ તો $r=..........$
A
$4$
B
$5$
C
$6$
D
$7$
Solution
$_n{P_r} = 720\,.\,\left( {\begin{array}{*{20}{c}}
n \\
r
\end{array}} \right)$……….
$\frac{{n\,!}}{{(n – r)\,!}} = 6\,!\frac{{n\,!}}{{r\,!\,(n – r)\,!}}\,\,\,\,$
$\,1 = \frac{{6\,!}}{{r\,!}}\,\,\,\,\therefore \,\,\,r\,!\, = \,6\,!\,\,\,\,\,\therefore \,\,\,r = 6$
Standard 11
Mathematics
