Solveeit Logo
Login

Question

Mathematics Question on Binomial theorem

If n=5,n=5, then (nC0)2+(nC1)2+(nC2)2+.....{{{{(}^{n}}{{C}_{0}})}^{2}}+{{{{(}^{n}}{{C}_{1}})}^{2}}+{{{{(}^{n}}{{C}_{2}})}^{2}}+..... +(nC5)2+{{{{(}^{n}}{{C}_{5}})}^{2}} is equal to

A

250

B

254

C

245

D

252

Answer

252

Explanation

Solution

(nC0)2+(nC1)2+(nC2)2+.....+(nC5)2{{{{(}^{n}}{{C}_{0}})}^{2}}+{{{{(}^{n}}{{C}_{1}})}^{2}}+{{{{(}^{n}}{{C}_{2}})}^{2}}+.....+{{{{(}^{n}}{{C}_{5}})}^{2}}
=(5C0)2+(5C1)2+(5C2)2+(nC3)3+(5C4)4={{{{(}^{5}}{{C}_{0}})}^{2}}+{{{{(}^{5}}{{C}_{1}})}^{2}}+{{{{(}^{5}}{{C}_{2}})}^{2}}+{{{{(}^{n}}{{C}_{3}})}^{3}}+{{{{(}^{5}}{{C}_{4}})}^{4}} +(5C5)2+{{{{(}^{5}}{{C}_{5}})}^{2}}
=1+25+100+100+25+1=1+25+100+100+25+1
=252=252