Combinatorics Solution Explanation

  • M1★ M2 M3 M4 M5

    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! 🙂

  • M0★ M1★ M2★ M3★ M4★ M5

    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.

  • MOD

    @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).

  • M1★ M2 M3 M4 M5

    @西瓜 @audrey Thank you both for the awesome explanations 😄