NUST NET Maths · Maths · Permutations, combinations and probability. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
Both ideas count without listing. A permutation is an arrangement, so order matters: ABC and BAC are different. A combination is a selection, so order does not matter: a team of A, B and C is the same team in any order.
Start every question by asking whether swapping two chosen items gives something new. If yes, use permutations; if no, use combinations. Then use the counting principle: multiply the numbers of ways for steps done one after another (and), add the numbers for separate cases (or).
Conditions are handled by simple tricks. Items that must stay together are tied into one block. Items that must stay apart are placed in the gaps between the others.
Using permutations for a selection. Choosing a committee or a handshake pair has no order, so use nCr; choosing people for named posts (captain and vice-captain) has order, so use nPr.
Answer: 720
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