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From the menu above, a restaurant offers customers two choices of appe
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23 Mar 2021, 05:54
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From the menu above, a restaurant offers customers two choices of appetizer and one choice each of entrée and dessert. If the appetizers must be different from each other, how many different meal combinations are available to customers?
Re: From the menu above, a restaurant offers customers two choices of appe
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23 Mar 2021, 23:51
Since only 1 dessert and 1 entree is required in the menu, there are a total of 5x4=20 dessert and entree combinations possible
For appetizers, we need to pick any 2 appetizers at a time, only condition being that they should not be the same. We can do this in 6C2 ways = 15 ways
Hence the total number of combinations possible are 15*20=300
From the menu above, a restaurant offers customers two choices of appe
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09 Sep 2022, 00:37
We apply the fundamental counting principle which says that if there are \(n\) ways of doing something, and \(m\) ways of doing another thing after that, then there are \(n∗m\) ways to perform both of these actions.
There are \(4\) ways of choosing an Entree
There are \(5\) ways of choosing a Dessert
There are \(6C2\) ways of choosing an Appetizer
Total number of meal combinations available \(= 4 * 5 * 6C2 = 4 * 5 * 6!/(6-2)! * 2! = 4 * 5 * 15 = 300\)