Arranging people in a line, and forming codes and numbers
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 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
- Order matters
- Arrangements in a line
- Keep them together
Read the transcript of the teaching part
Last time
Before we start: last time, in Arrangements and selections, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
Order matters
Nine people stand in a line. A code is typed on a keypad. In both, order matters, and some rules restrict who can go where. The trick is always the same: handle the restriction first, then count what is left. And when the restriction is difficult, count everything and subtract the arrangements you do not want.
Arrangements in a line
n different people can stand in a line in n factorial ways. Five people: 5 times 4 times 3 times 2 times 1, which is 120. To choose r from n in order, use n P r, which is n factorial over n minus r factorial. It counts ordered selections. Compare ordered with unordered: choosing a team uses combinations, but arranging people in a line uses permutations.
Keep them together
To keep two people together, treat them as a single block. Nine people become 8 objects: 8 factorial ways. Then the pair can swap inside the block: times 2. So together is 2 times 8 factorial, which is 80640. Not together is total minus together: 9 factorial minus 2 times 8 factorial, which is 282 240.
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.