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Q.

If ‘n’ is an integer between 0 and 21, then the minimum value of n!(21−n)!  is

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a

9!2!

b

10!11!

c

20!

d

21!

answer is B.

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Detailed Solution

n!(21−n)!=21!.n!.(21−n)!21!=21!.121Cn=21!21Cn For minimum value 21Cn  will be maximum. Maximum value of 21Cn= 21C10  ∴  Maximum value =21!21C10=21!21!×10!11!=10!11!
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If ‘n’ is an integer between 0 and 21, then the minimum value of n!(21−n)!  is