The people in charge of a raffle are going to give out four

The people in charge of a raffle are going to give out four prize bags to the raffle winners. They want to make sure that each prize bag contains at least one of the 11 gift certificates for a department store. In how many ways can the prize bags be prepared, assuming that all the gift certificates are of the same monetary value?

Solution

First put one gift certificate in each of the four bags

No of certificates left = 11 - 4 * 1 = 7 certificates

Now using beggars, there are 7 certificates and 4 bages

Then number of ways = C(n+r-1.r-1) = C(7+4-1,4-1) = 10C4

Hence number of ways = 10C3 = 10!/(7!3!) = (10*9*8)/3 = 240 ways