How to find the greatest or least number of combinations
Help Questions
SAT Math › How to find the greatest or least number of combinations
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
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.
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.
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.
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.
Refer to the above diagram.
How many different routes can be drawn that begin at Point A, then pass through, in order, Points B, C, A, B, C, and back to A, if no path between two points can be traveled twice?
Explanation
The multiplication principle can be applied here. There are 5 ways to get directly from Point A to Point B, 3 ways to get directly from Point B to Point C, and 2 ways to get directly from Point C to Point A. Since traveling the same path is not permitted, there are 4 ways left to get directly from Point A to Point B, 2 ways left to get directly from Point B to Point C, and 1 way left to get directly from Point C to Point A. Multiply these to get
8 people locked in a room take turns holding hands with each person only once. How many hand holdings take place?
28
21
15
24
Explanation
The first person holds 7 hands. The second holds six by virtue of already having help the first person’s hand. This continues until through all 8 people. 7+6+5+4+3+2+1=28.
Refer to the above diagram.
How many ways can a route be drawn that goes from Point A, to Point B, to Point C, then point A again, in that order?
Explanation
The multiplication principle can be applied here. There are 5 ways to get directly from Point A to Point B, 3 ways to get directly from Point B to Point C, and 2 ways to get directly from Point C to Point A. Multiply:
Refer to the above diagram.
How many ways can a route be drawn that goes from Point A, through Point B, to Point C, then back through Point B, and back to Point A? Any path between points can be taken twice.
Explanation
The multiplication principle can be applied here. There are 5 ways to get from Point A to Point B, 3 ways to get from Point B to Point C, 3 ways to get from Point C to Point B, and 5 ways to get from Point B to Point A. Multiply:
Mark has 5 pants and 7 shirts in his closet. He wants to wear a different pant/shirt combination each day without buying new clothes for as long as he can. How many weeks can he do this for?
4
5
6
7
8
Explanation
The fundamental counting principle says that if you want to determine the number of ways that two independent events can happen, multiply the number of ways each event can happen together. In this case, there are 5 * 7, or 35 unique combinations of pants & shirts Mark can wear. If he wears one combination each day, he can last 35 days, or 5 weeks, without buying new clothes.