1.How many different vertical arrangements are there of 10 flags if 5 are white, 3are blue, and 2 are red?

2.Assume we have an horse race with 12 horses. What is the possible number of combinations of 3 horses when the order matters and when it does not?

3. A die is thrown twice and the number on each throw is recorded. Assuming the dice is fair, what is the probability of obtaining at least one 6?

4. Jacob is taking two books along on her holiday vacation. With probability 0.4, he will like the first book; with probability 0.3, he will like the second book; and

with probability 0.2, he will like both books. What is the probability that he likes neither book?

5. For the month of June in the city of Chicago 37% of the days are cloudy. Also in the month of June in the city of Chicago 21% of the days are cloudy and rainy.

What is the probability that a randomly selected day in June will be rainy if it is cloudy?

6. Suppose that you are worried that you might have a rare disease. You decide to get tested, and suppose that the testing methods for this disease are correct 99

percent of the time (in other words, if you have the disease, it shows that you do with 99 percent probability, and if you don't have the disease, it shows that you do

not with 99 percent probability). Suppose this disease is actually quite rare, occurring randomly in the general population in only one of every 10,000 people.

If your test results come back positive, what are your chances that you actually have the disease?