Quiz about CCG Review Day Probability/Counting Procedures

Question 1

James purchased 3 shirts, 3 jackets and 2 pairs of pants.  How many different outfits using a shirt, a jacket, and pants are possible?

Accepted Answer

18

Answer

8

Answer

54

Question 2

A menu has 6 different sandwiches, with 3 choices of potato chips, 3 types of salad and 5 different beverages. How many different lunch combinations consisting of a sandwich, chips, salad and beverage can be ordered?

Accepted Answer

270

Answer

30

Answer

17

Answer

90

Question 3

The value of 5! is ____.

Accepted Answer

120

Answer

25

Answer

15

Answer

720

Question 4

How many ways can a club select a president, vice president, and a secretary from a group of 5 people?

Accepted Answer

60

Answer

12

Answer

15

Question 5

How many ways ways can you arrange the letters in the word math?

Accepted Answer

24

Answer

15

Answer

4

Question 6

What is the probability that a student does not play on a sports team?

Accepted Answer

.5

Answer

.45

Answer

.55

Question 7

What is the probability of choosing a Honda?

Accepted Answer

.5373

Answer

.5970

Answer

.4627

Answer

.4030

Question 8

What is the probability that a student does play a sport given they do not play an instrument?

Accepted Answer

.2222

Answer

.2

Answer

.10

Answer

.5

Question 9

What is the probability that the person picked will be a boy given they speak german?

Accepted Answer

.7273

Answer

.4

Answer

.16

Answer

.22

Question 10

What is the probability that a randomly selected student plays sports and does not participate in community service?

Accepted Answer

$$\frac{4}{27}$$

Answer

$$\frac{4}{9}$$

Answer

$$\frac{4}{12}$$

Answer

$$\frac{9}{27}$$

Question 11

What is the probability that a randomly selected student plays sports given that they do not do community service?

Accepted Answer

$$\frac{4}{12}$$

Answer

$$\frac{4}{27}$$

Answer

$$\frac{4}{9}$$

Answer

$$\frac{4}{5}$$

Question 12

What is the probability that a randomly selected student does not do community service given they do not play sports?

Accepted Answer

$$\frac{8}{18}$$

Answer

$$\frac{12}{27}$$

Answer

$$\frac{8}{12}$$

Answer

$$\frac{8}{27}$$

Question 13

What is the probability that a student plays sports given that they do community service?

Accepted Answer

$$\frac{5}{15}$$

Answer

$$\frac{5}{9}$$

Answer

$$\frac{5}{27}$$

Answer

$$\frac{9}{15}$$

Question 14

Are the events "Sports" and "Community Service" independent?

Accepted Answer

Yes, because P(S) is the same as P(S|CS).

Answer

No, because P(S) is not the same as P(S|CS).

Answer

Yes, because P(S) is the same as P(CS|S).

Answer

No, because P(S) is not the same as P(CS|S).

Question 15

Determine whether the following scenarios are a permutation or a combination:

Selecting a lead and an understudy for a school play.

Accepted Answer

Permutation

Answer

Combination

Answer

Counting Principle

Question 16

In how many ways can 3 different vases be arranged on a tray?

Accepted Answer

6

Answer

3

Answer

9

Answer

12

Question 17

How many outfits are possible with 5 pairs of jeans, 8 t-shirts, and 2 pairs of shoes?

Accepted Answer

Counting Principle

Answer

Combination

Answer

Permutation

Question 18

How many 5-digit (numerical) passwords are possible for the school email system if the first digit cannot be 0?

Accepted Answer

90,000

Answer

11,424,400

Answer

10,967,424

Answer

9000

Question 19

Homecoming has 7 candidates for King. How many ways can a King and a First Runner-up be chosen to form the Festival Court?

Accepted Answer

42

Answer

23

Answer

840

Answer

3,628,800

Question 20

Student council has 24 members.  In how many different ways can a president, vice-president, treasurer, historian, and secretary be selected?

Accepted Answer

5,100,480

Answer

0

Answer

42,504

Answer

5.17 x 10²¹

Question 21

A team of 17 volleyball players needs to choose three players to refill the water cooler.  How many different ways can the players be chosen?

Accepted Answer

680

Answer

3360

Answer

560

Answer

4080

Question 22

Picking a team of three people out of a group of 10.

Accepted Answer

Combination

Answer

Permutation

Answer

Counting Principle

Question 23

Choosing 3 toppings for your sundae out of a list of 15.

Accepted Answer

Combination

Answer

Permutation

Answer

Counting Principle

Question 24

Picking a President, Vice-President, and Secretary from a group of 12.

Accepted Answer

Permutation

Answer

Combination

Answer

Counting Principle

Question 25

How many outfits are possible with 5 pairs of jeans, 8 t-shirts, and 2 pairs of shoes?

Accepted Answer

Counting Principle

Answer

Permutation

Answer

Combination

Question 26

How many 2-digit numbers can you make using the digits 1, 2, 3, & 4 without repeating the digits?

Accepted Answer

12

Answer

90

Answer

100

Answer

24

Question 27

What is the probability that a student does play a sport and they do not play an instrument?

Accepted Answer

.10

Answer

.2

Answer

.2222

Answer

.5

Question 28

What is the probability that a student plays sports or that they do community service?

Accepted Answer

$$\frac{19}{27}$$

Answer

$$\frac{5}{9}$$

Answer

$$\frac{5}{27}$$

Answer

$$\frac{9}{15}$$

Question 29

What is the probability that a randomly selected student plays sports and does community service?

Accepted Answer

$$\frac{5}{27}$$

Answer

$$\frac{4}{27}$$

Answer

$$\frac{9}{27}$$

Answer

$$\frac{4}{5}$$

Question 30

What is the probability that a randomly selected student does not do community and does not play sports?

Accepted Answer

$$\frac{8}{27}$$

Answer

$$\frac{12}{27}$$

Answer

$$\frac{22}{27}$$

Answer

$$\frac{8}{18}$$

Question 31

What is the probability that a student does not play on a sports team and plays an instrument?

Accepted Answer

0.15

Answer

.5

Answer

.45

Answer

.55

Question 32

What is the probability that a student does not play on a sports team or does not play an instrument?

Accepted Answer

.6

Answer

.5

Answer

.45

Answer

0.15

Question 33

How would you solve?

From the 20 DVD's you purchased this past year, you plan to take five with you on vacation. How many different sets of five DVD's can you take? (Does the order you pack them in your backpack matter?)

Accepted Answer

Combination

Answer

Permutation

Answer

Counting Principles

Answer

Factorial

Question 34

The model of car you are thinking of purchasing is available in nine different colors, three different styles and two sizes of motor. How many ways can you order the car?

Accepted Answer

54

Answer

15

Answer

18

Answer

729

Question 35

How many ways can a stylist arrange 5 of 8 vases from left to right in a store display? (Since you are putting them in a specific order... P or C?)

Accepted Answer

6720

Answer

672

Answer

40

Question 36

Ambry must submit 4 paintings as part of her application to art school. If she has 25 to choose from, how many ways can she pick 4? (Does it matter the order of the 4 she picks??)

Accepted Answer

12,650

Answer

303,600

Answer

100

Answer

254

Question 37

Picking a team of three people out of a group of 10.

Accepted Answer

Combination

Answer

Permutation

Answer

Neither

Question 38

A four-unit passcode is created by choosing two digits and then two letters. How many unique passcodes exist if no number or letter can be repeated? (10 digits, 26 letters)

Accepted Answer

58,500

Answer

16

Answer

10,000

Answer

67,600

Question 39

Evaluate ₁₀P₃

Accepted Answer

720

Answer

3,628,800

Answer

5,040

Answer

120

Question 40

Evaluate ₁₂C₄

Accepted Answer

495

Answer

479,001,600

Answer

40,320

Answer

11,880

Question 41

Evaluate ₇C₇

Accepted Answer

1

Answer

5040

Answer

49

Answer

7

Question 42

Four names will chosen randomly from a list of twenty entries to be in a group that travels to Europe. How many unique possibilities are there? (Does order matter if it is who wins the trip?)

Accepted Answer

4,845

Answer

80

Answer

116,280

Answer

160,000

Question 43

What does ₁₀P₅mean?

Accepted Answer

Permutations with 10 choices and 5 positions

Answer

Permutations with 5 choices and 10 positions

Answer

Permutations with 5 numbers and 10 operations

Answer

Permutations with 5 hot dogs and 10 drinks

Question 44

Jessica wants to purchase the latest CD's from Twenty-One Pilots, Catfish & the Bottlemen, Weezer, Panic! at the Disco, Hozier and Young the Giant. However, she only has enough money for four CD's. In how many ways can she purchase four CD's?

Accepted Answer

15

Answer

24

Answer

360

Answer

90

Question 45

P(like vanilla or like football) =

Accepted Answer

60/72

Answer

50/72

Answer

42/72

Answer

32/72

Question 46

P(Pants given sandals):

Accepted Answer

4/20

Answer

6/15

Answer

1/2

Answer

2/7

CCG Review Day Probability/Counting Procedures

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