A company distributed a large number of lottery tickets to their customers. It is known that 20% of the tickets are winning tickets which can be exchanged for a prize. Each customer is entitled to only one lottery ticket.
(i) A group of 15 customers is randomly chosen. Show that the probability that at least 3 customers will each win a prize is 0.602.
Hence, find the probability that at most 5 customers will each win a prize given that at least 3 customers will each win a prize.
(ii) Find the probability that among three randomly chosen groups of 15 customers, there is one group with at least 3 customers that will each win a prize and two other groups with not more than 2 customers that will each win a prize.
How should I go about doing part (ii) of this question?
Heres my attempt at it:
First, I found the probability of:
1) P(X>=3) [at least 3 customers] and
2) P(X<=2) [not more than 2 customers]
and then i got stuck.