Counting: permutations and combinations: watch it solved step by step

Factorials, permutations (order matters), combinations (order does not) and arrangements of a word with repeated letters. Level: A-level. Type any problem of this kind and the Lab works it out and animates every move, with a plain-words explanation of why.

Worked example: 10P3

  1. The question. Permutations: choose 3 things from 10 and put them in order. Order matters, so ABC and CBA count as different.
  2. The formula. Choose the first place from n, the second from n-1, and so on for r places.
  3. Substitute and cancel. Most of 10! cancels with (10-3)!: only the first 3 factors survive.
  4. Check. Permutations are combinations times the number of ways to order the chosen things.

Answer: 720 permutations

Practise counting: permutations and combinations with problems the Lab marks for you.

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