In all of the following questions 7 coupons are being distributed into 4 showbags. In each case determine the number of ways it can be done, showing...

6. In all of the following questions 7 coupons are being distributed into 4 showbags. In each case determine the number of ways it can be done, showing working.

(c) Suppose that there are 4 different types of show bag and the coupons are identical and the bags are non-empty.

(d) Suppose the coupons and bags are both distinct but the bags are allowed to be empty.

8. Suppose that there is a prize ceremony awarding prizes to 10 finalists. Each finalist is going to get exactly one prize, but assume that each has an equal probability of receiving any given prize. The grand prize is $5000, there are 2 prizes of $2000, 2 prizes of $1000 and 5 prizes of $200. Let X represent the amount of money won by one prize recipient. Find E(X), var(X) and σ for X.

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