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Combinations - Problem 2
An application of choose is what we're going to look at now involving a catering menu. So you order from the caterers and they give you some choices. You can order 3 out of the 7 appetizers that they make, 4 out of the 12 mains and 3 out of the 5 desserts and the question is how many different orders could possibly be made?
So the trick here is that order doesn't matter for our order if that makes any sense that the order that we place it. So if you order appetizer 1 and then appetizer 2, you're going to get the exact same thing as if you switch that order.
So basically what we're doing is we're choosing this number of things out of this number of options, so for our appetizers, what we end up with is 7 choose 3, for our main courses we end up with 12 options and choosing 4 of them and for desserts we end up with 5 options choosing 3 of those, and we multiply in between because for each dessert pairing we could have a different entree pairing.
So we multiply 7 choose 3 times 12 choose 4 times 5 choose 3. I'm not going to go ahead and calculate this out hopefully you know the formula basically you're going to go whatever this term is factorial divided by difference between these two factorial and the second term factorial. You do that for each of these three terms. You're going to get a really big number, but basically what I was concerned with is the set up which is just going to be this product.