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Combinations  Problem 2
Carl Horowitz
Carl Horowitz
University of Michigan
Runs his own tutoring company
Carl taught upperlevel math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!
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.
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Carl Horowitz
B.S. in Mathematics University of Michigan
He knows how to make difficult math concepts easy for everyone to understand. He speaks at a steady pace and his stepbystep explanations are easy to follow.
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Combinations
Problem 1 6,672 viewsHow many ways to choose 3 students from a class of 20.

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Problem 2 5,744 viewsA catering menu gives you the choice of 3 out of 7 apps, 4 out of 12 main courses, and 3 out of 5 desserts.
How many different orders? 
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Problem 3 5,184 viewsIn a recent school election 40 students voted for candidate A and 60 voted for candidate B.
If 8 students are chosen at random find the probability 5 voted for candidate B? 
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Problem 4 5,105 viewsFind the probability of being dealt a heart flush in poker.
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