Permutations and Combinations

You will be able to

• Distinguish an arrangement (order matters, ⁿPᵣ) from a selection (order does not matter, ⁿCᵣ), and explain why ⁿCᵣ = ⁿPᵣ ÷ r!.
• Calculate the number of selections with a condition, such as exactly k women, by multiplying the combinations for each group.
• Calculate “at least one” counts as the total minus the selections with none, and handle a person who must, or must not, be chosen.

You will be able to

• Calculate the number of arrangements of r objects from n distinct objects with the box method, and write it as ⁿPᵣ = n! ÷ (n − r)!.
• Determine the number of arrangements with a restriction by filling the restricted box first, or by gluing objects that must be together into one block and multiplying by their internal arrangements.
• Calculate the number of arrangements in which two objects are not together as the total minus the arrangements in which they are together.