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LearnCambridge97092026–2027Paper 5 · Probability & Statistics 1Permutations and combinations

Paper 5 · Module

Permutations and combinations

3 subtopics≈ 100 min in total

Start the module: Arrangements and factorials Open graphing calculator

Arrangements and factorials
How many ways can things be put in order? Multiply the number of choices for each place, which gives $n!$ for $n$ different objects, then divide out the orderings you cannot tell apart.
≈ 30 min
Arrangements with restrictions
"Must be at the end", "must be together", "must not be next to each other": deal with the fussy conditions first, then arrange everything else freely. Glue objects together, or slot them into the gaps.
≈ 35 min
Selections (combinations)
When order does not matter, count with $^nC_r$ . Split selections into cases, use "at least one $=$ total $-$ none", and turn counts into probabilities by dividing by the total number of selections.
≈ 35 min