Find the value of nC0 - nC1 + nC2 - nC3 +.................+(-1)^n nCn
Expand (1+x)^n = (nC0) + (nC1) x +(nC2) x^2 + (nC3)x^3 +...(nCn)x^n
Put x = -1 in both sides
(1-1)^n = (nC0)-(nC1)+(nC2)-(nC3)+...+ (nCn)(-1)^n
so, (nC0)-(nC1)+(nC2)-(nC3)+...+(nCn)(-1)^n = 0