Glossary of terminology

Definition

Example

Addition principle (OR rule)

The number of ways in which either choice $A$ or choice $B$ can be made is the sum of the number of options for $A$ and the number of options for $B$. If $A$ and $B$ are mutually exclusive then: $n(A{\text{ OR }}B)=n(A)+n(B)$

By the addition principle, the number of ways of getting an even number on the first die or a multiple of three on the second die is 3 + 2.

Combination

A way of choosing a set of objects where the order does not matter. The number of ways of choosing $r$ objects out of $n$ is: ${n \choose r}={\frac {n!}{r!(n-r)!}}$

There are 56 ways of choosing three people from a group of eight.

Exclusion principle

Counting the number of outcomes that satisfy a given condition by first counting everything which does not satisfy the condition and then subtracting this from the total number of outcomes.

If out of 712 possible committees 16 involve both Thaïs and Gomer, by the exclusion principle 696 do not involve both Thaïs and Gomer.

Permutation

A way of arranging a set of objects in a particular order. The number of ways of arranging $n$ objects is $n!$: $n!=n(n-1)(n-2)...\times 2\times 1$

There are 24 possible permutations of the letters in the word CARS.

Product principle (AND rule)

The number of ways in which both choice $A$ and choice $B$ can be made is the product of the number of options for $A$ and the number of options for $B$: $n(A{\text{ AND }}B)=n(A)\times n(B)$

By the product principle, the number of ways of getting an even number on the first die and a multiple of three on the second die is $3\times 2$.