At the grocery store, Cory has narrowed down his selections to 6 vegetables, 6 fruits, 7 cheeses, and 5 whole grain breads. He wants to use the Express Lane, so he can only buy 15 items. In how many ways can he choose which 15 items to buy if he wants all 6 fruits?

Question

Mathematics

Ruthie

14 March, 12:48

At the grocery store, Cory has narrowed down his selections to 6 vegetables, 6 fruits, 7 cheeses, and 5 whole grain breads. He wants to use the Express Lane, so he can only buy 15 items. In how many ways can he choose which 15 items to buy if he wants all 6 fruits?

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Answers (1)

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Mollie Brewer · Answer 1

48620

Step-by-step explanation:

There are 6 fruits and 18 non-fruits. Cory wants to buy all 6 fruits, and 9 of the 18 non-fruits.

The number of ways he can choose 6 fruits from 6 is ₆C₆ = 1.

The number of ways he can choose 9 non-fruits from 18 is ₁₈C₆ = 48620.

The total number of combinations is 1 * 48620 = 48620.