Question 1161704: A catering service offers 5 appetizers, 4 main courses, and 12 desserts. A customer is to select 4 appetizers, 3 main courses, and 10 desserts for a banquet. In how many ways can this be done?
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
Use the combination formula
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Order does not matter because any dish does not outrank another.
We have 5 appetizers overall, and can only select 4 of them, so n = 5 and r = 4
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 Factorials are where we start with the given value, count down til we get to 1, multiplying all along the way.
There are 5 ways to make select the 4 appetizers. Put another way: there are 5 ways to not select a certain appetizer. We will use this value later, so let x = 5.
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Repeat for the main courses
n = 4 main courses overall, r = 3 selections allowed
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Similar as before, we have four ways to not pick a main course (equivalent to picking the 3 other main courses). We'll use this value later, so let y = 4.
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Repeat for the desserts. We have n = 12 and r = 10 this time. Keep in mind that  is always true.
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 Note how the 10! terms cancel
There are 66 ways to select ten desserts from a pool of twelve. Let z = 66.
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The last step is to multiply the values of x, y, and z found earlier.
x*y*z = 5*4*66 = 1320
Answer: 1320
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