Combinatorics Solution Explanation
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Pretty standard combinatorics question:
Jenny has \(3\) skirts, \(2\) pants, and \(4\) shirts. How many ways can she create an outfit with one of the shirts, and either a skirt or pant?
Can someone please explain why the solution is \(20\)? Thanks!
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Hello.
She has 4 shirts to pick from. She can pick either a skirt or a pant and there are 3+2 = 5 of those total. So, there are five ways she can pick a skirt or pant.4x5 =20 ways total.
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@西瓜 Great explanation!
Adding on to that, this is something that's formally known as the "Multiplication Principle." It basically means that if you can break a task into two independent events (meaning the events don't depend on each other), and one event can happen in x ways, and another can happen in y ways, then the whole task can occur in xy ways. That might sound sort of convoluted, but in practice, it's more intuitive For example, if a meal consists of a main dish and a drink, and there are 3 main dishes and 2 drinks, there are 3 * 2 = 6 total meals! (There are other ways to double check this-- drawing a tree diagram or just listing them out are two possibilities)
Or, in your problem, one "event" is choosing a shirt, and the other is choosing a bottom (skirts or pants). There are 4 ways to choose a shirt and 3+2 = 5 ways to choose a bottom, so there are 4 * 5 = 20 ways to choose an "outfit" (top and bottom).
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