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Let f(n)=sum(k=1)^(n) k^2(n Ck)^ 2 then ...

Let `f(n)=sum_(k=1)^(n) k^2(n C_k)^ 2` then the value of f(5) equals

A

`1000`

B

`1250`

C

`1750`

D

`2500`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` `k^(n)C_(k)=n^(n-1)C_(k-1)`
`:.sum_(k=1)^(n)k^(2)("^(n)C_(k))^(2)`
`=n^(2)sum_(k=1)^(n)("^(n-1)C_(k-1))^(2)`
`=n^(2)("^(2n-2)C_(n-1))`
`:. F(5)=25("^(8)C_(4))=1750`
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