1. There are eight different jobs in a printer queue. Each job has a distinct tag which is a string of three upper case letters. The tags for the eight jobs are: {LPW, QKJ, CDP, USU, BBD, PST, LSA, RHR}

(a) How many different ways are there to order the eight jobs in the queue?

(b) How many different ways are there to order the eight jobs in the queue so that job USU comes immediately before CDP?

(c) How many different ways are there to order the eight jobs in the queue so that job USU comes somewhere before CDP in the queue, although not necessarily immediately before?

(d) How many different ways are there to order the eight jobs in the queue so that either QKJ or LPW come last?

(e) How many different ways are there to order the eight jobs in the queue so that QKJ is either last or second-to-last?

2. A fair coin is flipped 12 times. Since the coin is a fair coin, all of the outcomes are equally likely.

(a) What is the size of the sample space?

(b) What is the probability that at least one of the 12 flips comes up heads?

(c) What is the probability that the same number of flips come up heads as come up tails?

3. A pair of dice (one red and one blue) are thrown. Each die has six sides. The dice are fair, so each outcome is equally likely. What is the probability that the number that comes up on the blue die is one more than the number on the red die?

4. Three different colored dice (red, blue, and green) are thrown. Each die has six sides. The dice are fair so each outcome is equally likely. What is the probability that at least one of the die comes up 6?

5. 30 different jobs are distributed to 6 different printers.

(a) How many ways are there to distribute the jobs if there are no restrictions on the number of jobs that go to each printer?

(b) How many ways are there to distribute the jobs if the same number of jobs go to each printer?

(Note that it matters which job goes to which printer.)

6. A family has four daughters. Their home has three bedrooms for the girls. Two of the bedrooms are only big enough for one girl. The other bedroom will have two girls. How many ways are there to assign the girls to bedrooms?

7. A school cook plans her calendar for the month of February in which there are 20 school days. Unfortunately, she only knows how to cook ten different meals.

(a) How many ways are there for her to plan her schedule of menus for the 20 school days if there are no restrictions on the number of times she cooks a particular type of meal?

(b) How many ways are there for her to plan her schedule of menus if she wants to cook each meal the same number of times?