- In a race in which eight automobiles are entered and there are no ties, in how many ways can the first three finishers come in?

- An election ballot asks voters to select three city commissioners from a group of six candidates. In how many ways can this be done?

- The Senate in a certain state is comprised of 58 Republicans, 39 Democrats, and 3 Independents. How many committees can be formed if each committee must have 3 Republicans and 2 Democrats?

- You are dealt one card from a standard 52-card deck. Find the probability of being dealt a diamond.

- A group consists of six men and six women. Five people are selected to attend a conference.
- In how many ways can five people be selected from this group of twelve?
- In how many ways can five women be selected from the six women?
- Find the probability that the selected group will consist of all women.

- If you are dealt 33 cards from a shuffled deck of 52 cards, find the probability of getting two queens and on king.

- You are dealt one card from a 52-card deck. Find the probability that you are not dealt a king.

- You are dealt one card from a 52-card deck. Find the probability that you are dealt a king or a red card.

- The mathematics department of a college has 6 male professors, 12 female professors, 15 male teaching assistants, and 6 female teaching assistants. If a person is selected at random from the group, find the probability that the selected person is a professor or a male.