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Statement-1 : The expression n!(100 - n)...

Statement-1 : The expression `n!(100 - n)!` is maximum when `n = 50`.
Statement-2 : `.^(2n)C_(r)` is maximum when `r = n`.

A

Statement `-1` is True, Statement -2 is True, Statement `-2` is a correct explanation for Statement `-1`

B

Statement `-1` is True, Statement -2 is True, Statement `-2` is `NOT` a correct explanation for Statement `-1`

C

Statement `-1` is True, Statement `-2` is False

D

Statement `-1` is False, Statement `-2` is True

Text Solution

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The correct Answer is:
D
`n!(100 - n)! = (100!)/(.^(100)C_(n))`
`.^(2n)C_(r)` is max when `r = n`
`:. n!(100-n)! = (100!)/(.^(100)C_(n))`
Hence `n!(100 - n)!` will be max. when `n = 50`.
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