Markquill
Start free

CAIE A Level Mathematics 9709

Permutations and combinations questions

Exam-style questions on Permutations and combinations, ordered from foundation to challenge. Pick one, write your answer the way you would in the exam, and it comes back marked against the mark scheme, point by point.

Practise this topic free

Written by Markquill to follow the Cambridge International syllabus. Markquill is independent and is not affiliated with or endorsed by Cambridge International.

  1. 2 marksFoundationA committee of 3 members is to be chosen from a group of 12 people. How many different committees can be formed?
  2. 2 marksFoundationA committee of 3 members is to be chosen from 9 candidates. The positions are distinct (chair, secretary, treasurer). Find the number of ways to fill the positions.
  3. 2 marksFoundationA committee of 4 people is to be chosen from a group of 11 candidates. How many different committees can be formed?
  4. 2 marksFoundationFind the number of permutations of 3 objects selected from a set of 6 distinct objects.
  5. 3 marksStandardA committee is to be formed from a group of 10 men and 8 women. The committee must consist of 4 men and 2 women. In how many different ways can the committee be chosen?
  6. 3 marksStandardConsider a word consisting of 10 letters: the letter 'A' appears 3 times, the letter 'B' appears 3 times, and the remaining letters are all distinct and different from A and B. How many distinct arrangements of the…
  7. 3 marksStandardA word consists of 6 letters: there are 2 copies of the letter A, 2 copies of the letter B, and the remaining letters are all distinct from each other and from A and B. Find the number of distinct arrangements of the…
  8. 3 marksStandardThere are 7 people to line up in a row. Two of them, Ali and Bea, must stand together. How many different arrangements are possible?
  9. 4 marksChallengeThere are 5 distinct objects of type A and 4 distinct objects of type B. In how many ways can all 9 objects be arranged in a line if all objects of type B must be kept together as a block?
  10. 4 marksChallengeA group of 8 people, including Alice and Bob, are to be arranged in a line for a photograph. In how many different ways can they be arranged if Alice and Bob must NOT stand next to each other?
  11. 4 marksChallengeA shopkeeper has 2 different types of fruit and 4 different types of candy. He wants to display them in a row on a counter, but all the candies must be placed together. How many different arrangements are possible?