Questions

MATH Integrated Math II - Unit 35: Permutations and Combinations

Fundamental Counting Principle

1) True or False. The Fundamental Counting Principle states that if there are "m" ways that one event can occur and "n" ways that another event can occur, then multiply “m” times “n” to find the number of ways both events can occur.

True

False

Suppose three coins were tossed all at the same time. The tree diagram shown below shows the possibilities of tossing one coin, two coins, and three coins. Use the tree diagram to solve the next two problems.

2) If three coins are tossed at the same time, how many outcomes are possible?

a.) 4

b.) 8

c.) 16

d.) 32

e.) 64

3) If two coins are added (five coins) and all are tossed at the same time, how many outcomes are possible?

a.) 4

b.) 8

c.) 16

d.) 32

e.) 64

On Friday, February 20, 2004, the Ohio Bureau of Motor Vehicles (BMV) unveiled the new license plate, which included three-letter and four-number combinations. All license plates are equally likely. Use this information to solve the next two problems.

4) What is the number of possible license plates of this type in Ohio? Each letter or number may be used more than once.

4000 character(s) left
Your answer is too long.

5) Brandon's license plate does not contain any vowels (A, E, I, O, and U) or the number "5". There are how many different possibilities for Brandon’s license plate?

4000 character(s) left
Your answer is too long.

6) If a pair of dice is rolled one time, there are how many possible outcomes?

a.) 6

b.) 36

c.) 72

d.) 1, 296

e.) 7,776

7) Mrs. Murphy is planning a graduation party for her daughter. The meal for the party will include one main dish, one type of potato, and one vegetable from the list of choices shown below. How many different meals can Mrs. Murphy select?

a.) 12

b.) 24

c.) 36

d.) 48

Permutations

8) Fill in the blank: A permutation is an arrangement of objects in a __________ __________.

250 character(s) left
Your answer is too long.

9) Evaluate the factorial.

a.) 105

b.) 15

c.) 210

d.) 315

10) Compute the permutation.

a.) 56

b.) 336

c.) 70

d.) 40,320

11) Compute the permutation.

a.) 5

b.) 10

c.) 20

d.) 100

12) Compute the permutation.

a.) 105

b.) 210

c.) 2020

d.) 5040

13) How many ways can a baseball coach choose the first, second, and third batters in the lineup for a team of 15 players?

a.) 455

b.) 504

c.) 2,730

d.) 3,360

14) On a bench that seats five people, how many ways can five people be seated?

a.) 1 way

b.) 30 ways

c.) 60 ways

d.) 120 ways

e.) 180 ways

Combinations

15) A combination is an arrangement of objects in which order (is or is not) important.

a.) is

b.) is not

16) Evaluate the factorial.

a.) 105

b.) 15

c.) 210

d.) 315

17) Compute the combination.

a.) 56

b.) 336

c.) 70

d.) 40,320

18) Select the solution for the combination.

a.) 8 x 7

b.) 8 x 7 x 6 x 5 x 4

c.) 8 x 4

d.) 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

19) Compute the combination.

a.) 5

b.) 10

c.) 20

d.) 100

20) Compute the combination.

a.) 105

b.) 210

c.) 2020

d.) 5040

21) There are twenty-five bands attending the cavalcade of bands. Trophies are awarded to the top 3 bands. Assuming all bands perform equally, there are how many possible ways that the trophies can be awarded?

a.) 300

b.) 600

c.) 2,300

d.) 13,800

22) Antonio’s Pizza Shop offers nine different toppings for a pizza. A customer may choose three toppings without any additional charge. How many different ways can a pizza at regular price be prepared?

a.) 84

b.) 27

c.) 126

d.) 504

Permutations and Combinations

23) When working with permutations and combinations, (a) what is similar about them and (b) what is different about them?

4000 character(s) left
Your answer is too long.

Attachments

There are no attachments

Attach a File

For the next four problems, choose whether each situation is a permutation or combination.

24) choosing any five CDs from a group of twenty

a.) permutation

b.) combination

25) seating twenty people in a row at a movie theater

a.) permutation

b.) combination

26) randomly selecting a team of 8 players from 12 players

a.) permutation

b.) combination

27) randomly listing the top ten finalists chosen to win a car from 1000 entries

a.) permutation

b.) combination

28) Six graduates can be “lined up” in how many different ways for graduation?

a.) 6

b.) 120

c.) 240

d.) 720

29) If six graduates attend an after-graduation party, and each one had to shake everyone else's hand once, how many handshakes would take place?

a.) 6

b.) 15

c.) 120

d.) 720

30) The letters in the word "TRAPEZOID" can be arranged in how many ways? (Note: All letters will be used in each arrangement; but, no letter will be used twice.)

a.) 1

b.) 9

c.) 362,880

d.) 387,420,489

31) If you were directed by your school to complete Offline Activities for this course, please enter the information on the Log Entry form.

No offline activities found

0 Hour(s) & 0 Minute(s)

If you are NOT required to complete Offline Activities for this course, please check the box below.

I do not have any Offline Activities for this unit.

Attachments

There are no attachments

Attach a File