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09-1 - At the grocery store Giovanni has narrowed down his...

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Unformatted text preview: At the grocery store, Giovanni has narrowed down his selections to 7 vegetables, 4 fruits, 5 cheeses, and 8 whole grain breads. He wants to use the Express Lane, so he can only buy 20 items. In how many ways can he choose which 20 items to buy if he wants all 5 cheeses? Begin by thinking of this problem as a Fundamental Counting Principle problem. There are two slots to fill—a slot for the cheeses and a slot for the remaining grocery items needed. We need to determine how many ways there are to fill each slot; then we will multiply the number of possibilities for each slot to get the answer to the problem. To calculate the number of ways of choosing the 5 cheeses and the other 20 — 5 = 15 grocery items, we will use the combination formula since the order in which they are chosen does not matter. The number of ways to choose all 5 out of 5 cheeses is 5! 5! 5! C_ _ _ 5!(1) — 1. 55 5!(5_5)! 5!0! ...
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