1. Chapter 5 Probability
5.5
Counting Techniques

2. Multiplication Principle of Counting
If a task consists of a sequence of choices in which there are p selections for the first choice, q selections for the second choice, r selections for the third choice, and so on.
Then the task of making these selections can be done in the following number of different ways.

3. If a license plate consists of a letter, then 5 numbers, how many different types of license plates are possible?

4. If a license plate consists of a letter, then 5 numbers, how many different types of license plates are possible?

6. Suppose that you have 5 different trees that you wish to plant
Suppose that you have 5 different trees that you wish to plant. In how many different ways can the 5 trees be planted in a row?

7. A permutation is an ordered arrangement of n distinct objects without repetitions. The symbol nPr represents the number of permutations of n distinct objects, taken r at a time, where r < n.

9. Determine the value of 9P3.

10. Suppose a committee consists of 10 people
Suppose a committee consists of 10 people. In how many ways can the chair and vice-chair of the committee be chosen if the first person randomly selected is the chair and the second person randomly selected is the vice-chair.

11. A combination is an arrangement, without regard to order, of n distinct objects without repetitions. The symbol nCr represents the number of combinations of n distinct objects taken r at a time, where r < n.

13. Determine the value of 9C3.

14. The United States Senate consists of 100 members
The United States Senate consists of 100 members. In how many ways can 4 members be randomly selected to attend a luncheon at the White House?

16. A landscape architect has 3 Sugar Maples, 2 Weeping Willows, and 4 Green Ash trees to plant along a street in a new subdivision. In how many different ways can the trees be planted?

17. What is the probability of obtaining 3 of a kind when 5 cards are drawn from a standard 52-card deck?

18. What is the probability of obtaining 3 of a kind when 5 cards are drawn from a standard 52-card deck?
P(3 of a kind) =