Study Master, Chapter 5

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Study Master, Chapter 5

McGraw-Hill Ryerson Mathematics of Data Management, pp. 296–297

1. Eleven students are to receive awards and 15 students are to receive scholarships at the Commencement. Nineteen students in total are to receive awards or scholarships.

a) Use a Venn diagram to illustrate this situation.

b) How many students are to receive both an award and a scholarship?

2. For their final project in drama, 11 students are acting in the one-act play, The Death and Life of Sneaky Fitch, and 14 students are acting in The Importance of Being Earnest. Five students are acting in both plays.

a) Use a Venn diagram to calculate how many students are acting in only one play.

b) How many student actors are there in all?

3. For the upcoming graduation ceremony there is a variety of committees working. Of the 42 staff members, 16 are involved in the cafeteria committee, 14 are on the awards committee, and 13 are on the program committee. Five staff members are on both the cafeteria and awards committees, seven are on both the awards and program committees, and six are on both the cafeteria and program committees. Four staff members are on all three committees.

a) Display this information on a Venn diagram.

b) How many staff members, in total, are involved in the upcoming graduation ceremony?

4. Ten students are available to work on the graduate committee.

a) In how many ways can you choose three students to lead each of the decorations committee, the refreshments committee, and the greetings committee?

b) In how many ways can you choose three students to help out with the various committees?

c) How are the numbers in parts a) and b) related?

5. A teacher has one large table at the front of her class. The table has room for five students.

a) In how many ways can the teacher choose five students in her grade 11 class of 21 students?

Study Master, Chapter 5 [Continued]

b) In how many ways can the teacher choose five students in her grade 9 class of 30 students?

c) Should the teacher try all the possible combinations of students? Explain why or why not?

6. Lina has a China figurine, a glass figurine, and a soapstone bear. In how many ways can she choose one or more of these figurines to put on her shelf?

7. In how many ways can you elect a committee with at least one member appointed from a group of eight individuals?

8. Maya works in the school canteen and can order from a choice of three types of salads, two different types of burgers, and pizza slices with either pepperoni or cheese. How many different purchases can Maya make? Assume that Maya can buy multiples of any type of item.

9. Rewrite each of the following using Pascal’s formula.

a) 13C5 b) 16C5 + 16C6

10. Rewrite

x6 – 12x5y + 60x4y2 – 160x3y3 + 240x2y4 – 192xy5 + 64y6

in the form (a + b)n.

Study Guide

For help with a specific question or type of question, review the examples specified below.

Question /

Section

/ Refer to:
1 / 5.1 / Example 1
2 / 5.1 / Example 2
3 / 5.1 / Example 3
4 / 5.2 / Example 1
5 / 5.2 / Example 3
6 / 5.3 / Example 1
7 / 5.3 / Example 2
8 / 5.3 / Example 3
9 / 5.4 / Example 1
10 / 5.4 / Example 6