Factorials, permutations and combinations
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 1 worked example, 4 practice questions, 2 real past-paper questions with the answers explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
What this lecture covers
- How many ways to line up
- Factorials
- Permutations and combinations
Read the transcript of the teaching part
Last time
Before we start: last time, in Trigonometric equations and proving identities, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
How many ways to line up
Five friends queue for a photograph. Five choices for the first place, four for the second, and so on. That is five factorial: a hundred and twenty ways. Counting without listing is what permutations and combinations are for.
Factorials
n factorial is n times n minus one, times n minus two, down to one. Five factorial is a hundred and twenty. And zero factorial is defined to be one. They cancel nicely. Seven factorial over five factorial is seven times six: forty-two.
Permutations and combinations
A permutation is an arrangement where order matters. n P r is n factorial over, n minus r, factorial. A combination is a selection where order does not matter. n C r is n P r divided by r factorial. Five P three is sixty, and five C three is ten. Each group of three can be arranged six ways: ten times six is sixty.
How often it comes up
The whole chapter: Permutations and Combinations.
Chapter 11: Permutations and combinations
- Factorials, permutations and combinations 5 min
Also for O Level Additional Maths 4037
Which topics come up most in O Level Additional Maths 4037 past papers, counted from every paper since 2004.