Assertion :The expression $n! (20 - n)!$ is minimum where $n = 10$ Reason: $^{2 p} C_{r}$ is maximum where $r = p$ , where $p$ is a constant.

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Assertion is incorrect but Reason is correct

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Solution

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
Consider $^{20} C_{r}$ .
It is a binomial coefficient of the (r+1)th term of $(1 + x)^{20}$ .
Now we know that the greatest binomial coefficient is the binomial coefficient of middle term.
In this case the middle term will be $\frac{20}{2} + 1 = 11 t h$ term.
Coefficient will be
$=^{20} C_{10}$
$= \frac{20!}{10! .10!}$
Hence
$n! . (20 - n)!$ is minimum when $n = 10$ .

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Assertion :The expression n!(20−n)! is minimum where n=10 Reason: 2pCr is maximum where r=p, where p is a constant.

Assertion :The expression $n! (20 - n)!$ is minimum where $n = 10$ Reason: $^{2 p} C_{r}$ is maximum where $r = p$ , where $p$ is a constant.