Q93 / 160 · TS EAMCET 2014 · Mathematics

If $n$ is an integer with $0 \leq n \leq 11$, then the minimum value of $n !(11-1)$ ! is attained when a value of $n$ equals to

A
$11$
Correct answer
B
$5$
C
$7$
D
$9$

Solution

We know, ${ }^{11} C_n$ is maximum when $n=5$. $$ \therefore{ }^{11} C_n=\frac{11 !}{n !(11-n) !} $$ $\therefore n !(11-n) !$ is minimum when $n=5$.

Hence, the correct answer is option: 'B'.

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