NIMCET 2021 Question Paper with solutions

Question : 16 of 120

Marks: +1, -0

n

is an integer between 0 to 21 , then find a value of

n

for which the value of

n !(21-n) !

is minimum

Solution:

We know that

{ }^{{m}} {C}_{{n}}={{m} !}/{{n} !({m}-{n}) !}

{ }^{21} {C}_{{n}}={(21) !}/{n !(21-n) !}

n !(21-n) !={(21) !}/{{ }^{21} C_{n}}

This will be minimum when

{ }^{21} {C}_{n}

is maximum.
And

{ }^{21} {C}_{n}

is maximum
at

n=10

n=11

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