Draw a tree diagram showing all the possible outcomes (w1n', loss, or tie) in three games between two hockey teams. How many possible outcomes are there?

Octahedral dice have eight faces. Make a chart showing the sums of the faces on two dice. Which sum occurs most frequently? Which sums occur least frequently?

The heart honour cards (10, J, Q, K, A) are removed from a standard deck. Three cards are randomly selected from the heart honour 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?

A home security code requires five digits to be entered on a keypad.

a) How many distinct security codes are possible?

b) Sarah reset her security code but has forgotten it. If it takes her eight seconds per attempt, what is the maximum time it would take for her to find the correct code?

When ordering a gaming computer online, Ryan has three choices for processors, four choices for size of RAM, five choices for the video card, three choices for the hard drive. and two choices for the sound card.

a) How many choices does Ryan have when configuring his computer?

b) If there were an additional choice for the video card, how would it affect the total number of choices? Explain the difference.

Barb knits socks for a Charity supporting homeless and low income people. She likes to make striped socks and selects from s1x' different colours. The top stripe can be any colour. The second stripe may not match the first colour. The bottom colour may not match the second, but may match the first. How many distinct pairs of socks could Barb How many ways are there for a company to assign three different jobs to three of its five employees?make?

How many ways are there for a company to assign three different jobs to three of its five employees?

a) Evaluate each permutation and place them in the array as shown.

b) Extend the array by one row without using factorials. Explain how you did this.

c) Identify and describe two other patterns in the array.

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. In how many ways could she arrange the books?

In how many ways could the letters in the word STORAGE be arranged if the vowels must remain in

a) even positions?

b) odd positions?

c) even or odd positions?

In how many ways can you rearrange the letters in the word NATIVE if the vowels must not be together?

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

For a gift exchange, 10 people’s names are written on slips of paper and placed in a bowl. The slips of paper are mlx'ed up, and each person selects one name.

a) What is the probability that everyone selects their own name?

b) What is the probability that nobody selects his or her own name?

Six different coloured balls are placed in a box. Kendra and Abdul each select a ball without replacement.

a) What is the probability that Kendra selects the green ball and Abdul selects the red ball?

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

c) What is the probability that Kendra does not select the green ball and Abdul does not select the red ball?

If five people each select a letter from the alphabet with repetition permitted, what is the probability that they are

a) all the same?

b) all different?