Question

Each of the cereal boxes contains one of n differnt coupons, chosen
at random. if you buy k boxes, what is the probability that you
have a complete collection?

Answer #1

Total number of coupons = k as there is 1 coupon in each box.

Let the number of first type of coupon be X_{1}, second
type of coupon be X_{2} and so on till X_{n} as the
number of coupons which is n^{th} type of coupon.

Therefore, we have here:

X_{1} + X_{2} + ...... + X_{n} = k

As each one of them could be greater than or equal to 0. The total number of solutions here is given using the multinomial formula as:

Also given that we want the number of each type of coupon to be at least 1, therefore the number of solutions in that case is computed using the multinomial formula as:

Therefore the required probability here is computed as:

**This is the required probability here.**

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