Permutation / Combination

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SAT Math › Permutation / Combination

Questions 1 - 10
1

Shannon decided to go to nearby café for lunch. She can have a sandwich made on either wheat or white bread. The café offers cheddar, Swiss, and American for cheese choices. For meat, Shannon can choose ham, turkey, bologna, roast beef, or salami. How many cheese and meat sandwich options does Shannon have to choose from?

10

20

25

30

35

Explanation

2 bread choices * 3 cheese choices * 5 meat choices = 30 sandwich choices

2

An ice cream parlor serves 36 ice cream flavors. You can order any flavor in a small, medium or large and can choose between a waffle cone and a cup. How many possible combinations could you possibly order?

72

108

144

172

216

Explanation

36 possible flavors * 3 possible sizes * 2 possible cones = 216 possible combinations.

3

An ice cream parlor serves 36 ice cream flavors. You can order any flavor in a small, medium or large and can choose between a waffle cone and a cup. How many possible combinations could you possibly order?

72

108

144

172

216

Explanation

36 possible flavors * 3 possible sizes * 2 possible cones = 216 possible combinations.

4

Shannon decided to go to nearby café for lunch. She can have a sandwich made on either wheat or white bread. The café offers cheddar, Swiss, and American for cheese choices. For meat, Shannon can choose ham, turkey, bologna, roast beef, or salami. How many cheese and meat sandwich options does Shannon have to choose from?

10

20

25

30

35

Explanation

2 bread choices * 3 cheese choices * 5 meat choices = 30 sandwich choices

5

If a series of license plates is to be produced that all have the same pattern of three letters followed by three numbers, roughly how many alphanumeric combinations are possible?

1 thousand

18 thousand

11 million

18 million

180 million

Explanation

The total number of possible combinations of a series of items is the product of the total possibility for each of the items. Thus, for the letters, there are 26 possibilities for each of the 3 slots, and for the numbers, there are 10 possibilities for each of the 3 slots. The total number of combinations is then: 26 x 26 x 26 x 10 x 10 x 10 = 17,576,000 ≈ 18 million.

6

If a series of license plates is to be produced that all have the same pattern of three letters followed by three numbers, roughly how many alphanumeric combinations are possible?

1 thousand

18 thousand

11 million

18 million

180 million

Explanation

The total number of possible combinations of a series of items is the product of the total possibility for each of the items. Thus, for the letters, there are 26 possibilities for each of the 3 slots, and for the numbers, there are 10 possibilities for each of the 3 slots. The total number of combinations is then: 26 x 26 x 26 x 10 x 10 x 10 = 17,576,000 ≈ 18 million.

7

A baker has four different types of frosting, three different kinds of sprinkles, and 8 different cookie cutters. How many different cookie combinations can the baker create if each cookie has one type of frosting and one type of sprinkle?

15

24

48

96

Explanation

Since this a combination problem and we want to know how many different ways the cookies can be created we can solve this using the Fundamental counting principle. 4 x 3 x 8 = 96

Multiplying each of the possible choices together.

8

A baker has four different types of frosting, three different kinds of sprinkles, and 8 different cookie cutters. How many different cookie combinations can the baker create if each cookie has one type of frosting and one type of sprinkle?

15

24

48

96

Explanation

Since this a combination problem and we want to know how many different ways the cookies can be created we can solve this using the Fundamental counting principle. 4 x 3 x 8 = 96

Multiplying each of the possible choices together.

9

Gihani has six clean shirt and four pairs of pants to choose from. How many possible combinations of outfits can she make with these items?

Explanation

If she has six shirts and four pairs of pants, then the total number of options she has can be found by multiplication.

To double check, you can create a tree diagram, listing the possible combinations.

10

Gihani has six clean shirt and four pairs of pants to choose from. How many possible combinations of outfits can she make with these items?

Explanation

If she has six shirts and four pairs of pants, then the total number of options she has can be found by multiplication.

To double check, you can create a tree diagram, listing the possible combinations.

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