1. A jar contains 8 differently coloured balls. If you remove two balls, one at a time, how many different colour sequences are possible?

A) (82)!

B) 6!

C) 87

D) 8!

E) None of the above.

2. In arranging people around a circular table, we take into account their seats relative to each other,not the actual position of any one person. How many different ways can n people be arranged around the circular table?

A)n!

B)nn

C)2n!

D)n!1

E) None of the above.

3. Suppose five runners end a race with no ties. How many ways can the first, second, and third places be decided?

A) 10

B) 60

C) 20

D) 40

E) None of the above.

4. A jogger jogs every morning to her coffee shop, which is eight blocks east and five blocks south of her home. She always takes the shortest route, but she likes to vary it. How many different routes can she take?

A) 1287

B) 1716

C) 286

D) 715

E) None of the above

5. In an attempt to clean up your room, you have purchased a new floating shelf to put some of your 17 books you have stacked in a corner. These books are all by different authors. The new bookshelf is large enough to hold 10 of the books. How many ways can you arrange 10 books on your new shelf, if you insist that the books be placed in alphabetical order?

A) 6188

B) 12376

C) 24310

D) 19448

E) None of the above.

6. Ten people have been tested for HIV. How many ways are there for 6 of those 10 to test positive?

A)(610)

B) 60

C)P_10,6

D) 4

E) None of the above.