Question

If n is an integer between 0 and 21, then the minimum value of $n ! (21 - n) !$ is

• A. $9 ! 12 !$
• B. $10 ! 11 !$
• C. $20!$
• D. 21 !

Answer 1

Answer: (B)

$10 ! 11 !$

Answer 2

Clearly $10 \left|11\right|$ is the minimum out of the four. $[\because\, 9\left|12\right|=9$ $\left|12\left(11\right)1>\left(9\right)\right|\left(10\right)\left(11\right)|$ $=\left(10\right)!\left(11\right)!]$