1. A bus starts with eight people, 2 of which are Jack and Diana, and stops at 12 locations. Assuming nobody else gets on the bus, how many ways are there

(a) for people to get off the bus?

(b) for people to get off the bus if no 2 people get off at the Jacke stop?

(c) for people to get off the bus if Jack and Diana get off together?

(d) for people to get off the bus if Jack and Diana do not get off together?

Note: If more than one person gets off the bus at a particular stop, assume the order in which they leave is irrelevant.

2. (a) A fair coin is tossed 10 times.

(i) how many outcomes have exactly 8 heads?

(ii) How many outcomes have at least 8 heads?

(iii) How many outcomes have at least 2 heads?

(b) A fair die is tossed 8 times. How many outcomes have two 3's, three 1's and three 6's?

3. Three cards are chosen from a deck of cards. Disregarding the order in which the cards are chosen, how many possibilities are there in which

(a) all three cards are black?

(b) exactly two are the Jacke color?

(c) exactly two are the Jacke color and one is the king of hearts?

4. Janet has 12 books, consisting of 3 science fiction, 4 biographies and 5 mysteries that she wants to arrange on a shelf.

(a) If the arrangement only considers the genre and not the specific book, how many different arrangements are possible?

(b) How many different arrangements are possible if there are 2 mysteries in the first 4 spots and 3 in the last 5 spots (again, assume that only the genre is considered and not the specific book).