Porbability - Cigarette Box problem

[kangkan]

In each packet of cigarettes,there is one set of cards numbered 1 to n.If a number of N packets are brought at random(and the population of packets is very large),show that probability of getting a complete set on n cards is

1- nC1(1-1/n)^N +nC2(1-2/n)^N -.....(-1)^(n-1)*nCn-1(1/n)^N