Math, asked by rajeshkumar08283, 4 months ago

4. If nCa=nCb, find n​

Answers

Answered by MrBasic
4

Here,

{_n}C_a =  {_n}C_b\\\implies\frac{n!}{(n-a)!a!} =\frac{n!}{(n-b)!b!} \\\implies {(n-a)!a!}={(n-b)!b!}\\\implies (n-a)!a!=(n-a)!a!\:\:[a=b]\\\implies (n-a)!=(n-a)!\\\implies (n-a)(n-a-1)!=(n-a)(n-a-1)!\\\implies n-a = n-a\\\implies n-n = a-a\\\implies n(1-1)=0\\\implies n\times 0 = 0

Where is true for all values of n\in \mathbb{N}

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