Permutation and Combination, Glossary

Knowing the vocabulary of Permutation and Combination precisely is worth easy marks in SPM Add Math. Questions often turn on a single keyword, read it correctly and the method follows; misread it and even good algebra earns nothing.

Because the SPM paper is bilingual (BM/EN), each term below shows the English and Malay wording, so your child recognises it whichever way a question is phrased.

• Multiplication Rule, The multiplication rule states that if one task can be done in $m$ ways and a second in $n$ ways, then the two together can be done in $m\times n$ ways. It is the foundation of counting problems and extends to any number of successive independent choices. →
• Factorial, A factorial, written $n!$, is the product of all positive integers from $1$ up to $n$; for example $5!=5\times4\times3\times2\times1=120$. By definition $0!=1$. Factorials count the number of ways to arrange $n$ distinct objects in a row and appear in permutation and combination formulas. →
• Permutation, A permutation is an arrangement of objects in which the order matters. The number of ways to arrange $r$ objects chosen from $n$ distinct objects is ${}^{n}P_{r}=\frac{n!}{(n-r)!}$. Because order counts, $AB$ and $BA$ are treated as two different permutations. →
• Combination, A combination is a selection of objects in which the order does not matter. The number of ways to choose $r$ objects from $n$ distinct objects is ${}^{n}C_{r}=\frac{n!}{r!\,(n-r)!}$. Here $AB$ and $BA$ count as the same combination, since only the group chosen matters. →
• Circular Permutation, A circular permutation counts arrangements of objects around a circle, where only relative position matters because the ring can be rotated. For $n$ distinct objects the number of arrangements is $(n-1)!$, rather than $n!$, since one object can be fixed as a reference point. →
• Arrangement of Identical Objects, When some objects being arranged are identical, swapping them creates no new arrangement, so the total is reduced. The number of distinct arrangements of $n$ objects with repeats is $\frac{n!}{p!\,q!\,\dots}$, where $p, q, \dots$ count each repeated group. For example, the letters of BUKU arrange in $\frac{4!}{2!}$ ways. →

Do not just memorise definitions, practise using each term inside a full solution, the way a marker expects to see it. In the Permutation and Combination chapter especially, stating the right definition or condition in your working can itself earn a method mark.

Our teachers check that a student can both recall a term and deploy it fluently under exam conditions.

Vocabulary sticks best when it is tied to doing rather than reading. Instead of learning the Permutation and Combination terms as a flat list, meet each one inside a worked question and say the step aloud in words as you write it, a term you can use in a sentence is a term you understand.

It also helps to link related terms together rather than in isolation, since Permutation and Combination questions usually combine several ideas at once. Because the SPM paper is bilingual, glance once at the Malay and English wording of each term side by side, so the language a question is set in never throws you.

If a term keeps feeling slippery, that is usually a sign the underlying idea needs another look, not the word itself, and that is exactly the kind of gap a one-to-one lesson closes quickly.