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Question

If nr=0(nCr1nCr+ nCr1)3=2524, then the value of n is

A
10
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B
5
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C
20
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D
15
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Solution

The correct option is B 5
nCr+ nCr1= n+1Cr
nCr1nCr+ nCr1=nCr1n+1Cr
=n!(r1)!(nr+1)!(n+1)!r!(n+1r)!
=rn+1

nr=0(nCr1nCr+ nCr1)3=nr=0(rn+1)3
=1(n+1)3nr=0r3

nr=1r3=nr=0r3=(n(n+1)2)2
n24(n+1)=2524=524(5+1)
n=5

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