Question

C de 4 luate cate 0+C4 luate cate 1+ C de 4 luate cate 2+ C de 4 luate cate 3 +C de de 4 luate cate 4=2 la a 4

Answer 1

$C_4^0+C_4^1+C_4^2+C_4^3+C_4^4=1+\frac{4!}{1!(4-1)!}+\frac{4!}{2!(4-2)!}+\frac{4!}{3!(4-3)!}+1=\\\\=2+\frac{4!}{3!}+\frac{4!}{2!\cdot2!}+\frac{4!}{3!}=2+2\frac{3!\cdot4}{3!}+\frac{2!\cdot3\cdot4}{4}=2+8+6=16=2^4$