1. Octahedral dice have eight faces. Make a chart showing the sums of the faces ontwo dice. which sum occurs most and least frequently?

2. Andy knits socks for a charity supporting homeless and low income people. She likes to make striped socks any selects from six different colors. The top stripe can be any color. The second stripe may not match the first color. The bottom color may not match the second, but may match the first. Decide how many distinct pairs of socks could Andy make?

3. A bookstore clerk is arranging seven novels, four plays, and five poetry books in a display case. Each type of book remains in its own group, but the groups can be in any order. Calculate how many ways could she arrange the books?

4. Complete how many five-digit even numbers can formed using all the digits 0, 1, 2, 3 and 4?

5. If five people each select a letter from the alphabet with repetition permitted, solve the probability that they are. a) All the same?b) All different?

6. The heart honor cards (10, J, Q, K, A) are removed from a standard deck. Three cards are randomly selected from the heart honor cards without replacement

a) Illustrate all the possible outcomes using a tree diagram.

b) Highlight the path that indicates the run queen of hearts, king of hearts, ace of hearts.

c) How many possible outcomes are there?

7. Six different colored balls are placed in a box. James and his best friend tom select a ball without replacement

a) What is the probability that James selects the green and tom selects the red ball?

b) What is the probability that James selects the green ball and tom does not select the red ball?

c) What is the probability that James does not select the green ball and tom does not select the red ball?

8. There are 25 men and 20 women who belong to a club. An executive panel consisting of a president, vice president, secretary, and treasurer is being chosen.

a) In how many ways could the executive panel be chosen with no restrictions?

b) In how many ways could the executive panel be chosen is it must include at at least one woman and one man?

c) In how many ways could the executive panel be chosen is the president and vice president must have different genders?

9. a general guideline explaining when to use the fundamental counting

principle and when to use the rule of sum for permutations. Include a similar

example for each.

10. How is 12P3 different from 12P1 3? Use examples to help distinguish between

the two.

11. Consider a spinner with four sections. Represent the outcomes of three spins by

using the tree diagram.

12. Use an example to demonstrate the fundamental counting principle.

13. Which would have more possibilities, arranging r people from a group of n people

with regard to order or without regard to order?