IB/Group 5/Mathematics/Higher/Glossary of terminology

Template:Status Template:Multicol Template:Multicol-break Definition Template:Multicol-break Example Template:Multicol-end

Addition principle (OR rule)

Template:Multicol-break 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:

$n(A\text{ OR }B)=n(A)+n(B)$ Template:Multicol-break 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. Template:Multicol-end

Combination

Template:Multicol-break 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:

$(\genfrac{}{}{0ex}{}{n}{r})=\frac{n!}{r!(n-r)!}$ Template:Multicol-break There are 56 ways of choosing three people from a group of eight. Template:Multicol-end

Exclusion principle

Template:Multicol-break 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. Template:Multicol-break If out of 712 possible committees 16 involve both Thaïs and Gomer, by the exclusion principle 696 do not involve both Thaïs and Gomer. Template:Multicol-end

Permutation

Template:Multicol-break A way of arranging a set of objects in a particular order. The number of ways of arranging $n$ objects is $n!$:

$n!=n(n-1)(n-2)...\times 2\times 1$ Template:Multicol-break There are 24 possible permutations of the letters in the word CARS. Template:Multicol-end

Product principle (AND rule)

Template:Multicol-break 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 $B$:

$n(A\text{ AND }B)=n(A)\times n(B)$ Template:Multicol-break 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 $3\times 2$. Template:Multicol-end