Arrangements and selections
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 2 worked examples, 5 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?
- Arrangements in a line
Read the transcript of the teaching part
Last time
Before we start: last time, in Cumulative frequency graphs, histograms with unequal widths, mean and median, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
How many ways?
A committee, a password, a queue for a bus. In each case someone asks how many ways there are, and listing them would take for ever. The skill is to decide first whether order matters, and then to count with factorials and combinations.
Arrangements in a line
n different objects can be arranged in a line in n factorial ways. Choosing and arranging r of n different objects gives n P r, which is n factorial over n minus r factorial. If some objects are identical, divide by the factorial of each repeat. TELESCOPE has three E's.
How often it comes up
How often Cambridge has asked each part, counted by ExamYard from every past paper in its question bank: Arranging letters of a word · Selections with conditions.
The whole chapter: Permutations and Combinations.
Chapter 5.2: Permutations and combinations
- Arrangements and selections 5 min
- Arranging people in a line, and forming codes and numbers 6 min
Also for A Level Maths 9709 Paper 5
Which topics come up most in A Level Maths 9709 Paper 5 past papers, counted from every paper since 2004.