If n=5, then (nC0)2+(nC1)2+(nC2)2+..... +(nC5)2 is equal to

Question

If n=5, then (nC0)2+(nC1)2+(nC2)2+..... +(nC5)2 is equal to (A) 250 (B) 254 (C) 245 (D) 252

Tardigrade Admin · Accepted Answer

(nC0)2+(nC1)2+(nC2)2+.....+(nC5)2 =(5C0)2+(5C1)2+(5C2)2+(nC3)3+(5C4)4 +(5C5)2 =1+25+100+100+25+1 =252

Q. If $n = 5,$ then $(^{n} C_{0})^{2} + (^{n} C_{1})^{2} + (^{n} C_{2})^{2} + .....$ $+ (^{n} C_{5})^{2}$ is equal to