IXL - Combinations and permutations: word problems (Algebra 2 practice)

Brianna is planning her day at the beach. This afternoon, she can go for a swim or fly a kite. For dinner, she can go to the hamburger joint or the fish restaurant. For dessert, she can go to the pie house or the fudge factory. Given these choices, how many different combinations does Brianna have to choose from?

combinations

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Learn with an example

question

Ron is arranging cheeses in a row on a cheese board. The cheeses he has are Colby, Muenster, and Gorgonzola. In how many different orders can Ron arrange them?

orders

key idea

To find out how many different orders are possible, use a factorial. A factorial is a whole number followed by an exclamation point. To evaluate a factorial, multiply all the whole numbers between 1 and the given number.

solution

There are 3 cheeses: Colby, Muenster, and Gorgonzola.

Ron could arrange the cheeses in 3! different orders.

3! = 3 × 2 × 1 = 6

You can check your answer by making a list. Call the 3 cheeses A, B, and C. See how many different orders are possible.

ABC
ACB
BAC
BCA
CAB
CBA

You get the same answer either way. Ron could arrange the cheeses in 6 different orders.

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Combinations

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