Maths · Rung 19 of 30

Combinatorics

There are n! ways to order n different things (4! = 24). Choosing k out of n regardless of order is a combination: C(5, 2) = 10. If order matters, it is a permutation: 5 × 4 = 20. And when you make one choice and then another, the options multiply.

Where this sits

This is where the ladder starts: nothing is needed before it.

Exercises from this rung

Generated by the app, from easiest to hardest

  1. In how many ways can 4 books be arranged on a shelf?

    • 24
    • 120
    • 16
    • 6

    Why For the first place there are 4 books, for the second 3, and so on: 4! = 4 × 3 × 2 × 1 = 24.

    easier

  2. In how many ways can 3 books be arranged on a shelf?

    • 9
    • 24
    • 2
    • 6

    Why For the first place there are 3 books, for the second 2, and so on: 3! = 3 × 2 × 1 = 6.

    in between

  3. 6 runners. In how many ways can gold and silver be awarded?

    • 30
    • 12
    • 15
    • 36

    Why There are 6 options for gold and 5 left for silver: 6 × 5 = 30. Not 15: here order matters.

    harder