Permutations and combinations: past paper questions

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• Question 5May/June 2026, paper 51Structured10 marks

  Three letters are chosen at random from the 9 letters in the word RETRIEVES. Find the probability that at least one of the letters is an E.

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• Question 7Oct/Nov 2025, paper 51Structured10 marks

  How many different arrangements are there of the 10 letters in the word SEYCHELLES?

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• Question 7Oct/Nov 2024, paper 51Structured9 marks

  How many different arrangements are there of the 9 letters in the word INTELLECT in which the two Ts are together?

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• Question 6Oct/Nov 2023, paper 51Structured10 marksHas a diagram

  In a restaurant, the tables are rectangular. Each table seats four people: two along each of the longer sides of the table (see diagram). Eight friends have booked two tables, $X$ and $Y$.

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• Question 1May/June 2026, paper 52Structured6 marks

  A club has 15 members made up of 6 men and 9 women. Every Friday a team of 5 members is selected at random to represent the club in a competition. Find the probability that next Friday the team will consist of more men than women.

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• Question 7Oct/Nov 2025, paper 52Structured10 marks

  Find the number of different arrangements of the 10 letters in the word ZOOLOGICAL in which the three Os are together and the two Ls are not next to each other.

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• Question 2Oct/Nov 2024, paper 52Structured4 marks

  Find the number of different arrangements of the 9 letters in the word ALGEBRAIC.

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• Question 7Oct/Nov 2023, paper 52Structured10 marks

  Find the number of different arrangements of the 9 letters in the word ANDROMEDA in which no consonant is next to another consonant.

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• Question 2Oct/Nov 2025, paper 53Structured4 marks

  The Splash Club has 26 members, of whom 16 are swimmers and 10 are divers. No member is both a swimmer and a diver. The club committee consists of 6 of these 26 members.

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• Question 5Oct/Nov 2024, paper 52Structured6 marks

  In a class of 21 students, there are 10 violinists, 6 guitarists and 5 pianists. A group of 7 is to be chosen from these 21 students. The group will consist of 4 violinists, 2 guitarists and 1 pianist.

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• Question 6Oct/Nov 2023, paper 53Structured10 marks

  Jai and his wife Kaz are having a party. Jai has invited five friends and each friend will bring his wife. At the beginning of the party, the 12 people will stand in a line for a photograph.

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• Question 6May/June 2026, paper 53Structured10 marks

  Find the number of different arrangements of the 10 letters in the word POSSESSION in which the four Ss are all next to each other and the two Os are not next to each other.

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• Question 3Oct/Nov 2025, paper 53Structured6 marks

  Find the number of different arrangements of the 9 letters in the word DAFFODILS in which there is a D at each end and the two Fs are not next to each other.

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• Question 6Oct/Nov 2024, paper 53Structured11 marks

  Find the number of different arrangements of the 9 letters in the word HAPPINESS.

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• Question 2May/June 2023, paper 51Structured5 marks

  Find the number of ways in which a committee of 6 people can be chosen from 6 men and 8 women if it must include 3 men and 3 women.

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• Question 2May/June 2025, paper 51Structured7 marks

  Find the number of different arrangements of the 8 letters in the word KANGAROO in which the two As are together and the two Os are not together.

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• Question 7May/June 2024, paper 51Structured10 marks

  The eight digits 1, 2, 2, 3, 4, 4, 4, 5 are arranged in a line. How many different arrangements are there of these 8 digits?

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• Question 3May/June 2023, paper 51Structured6 marks

  Find the number of different arrangements of the 8 letters in the word COCOONED.

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• Question 5May/June 2025, paper 51Structured7 marks

  In a group of 20 musicians, there are 9 guitarists, 6 pianists and 5 drummers. 6 musicians are selected from these 20 to perform at a concert.

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• Question 7May/June 2024, paper 52Structured10 marks

  How many different arrangements are there of the 10 letters in the word REGENERATE?

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• Question 6May/June 2023, paper 52Structured10 marks

  In a group of 25 people there are 6 swimmers, 8 cyclists and 11 runners. Each person competes in only one of these sports. A team of 7 people is selected from these 25 people to take part in a competition.

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• Question 6May/June 2025, paper 52Structured9 marks

  Find the number of different ways in which the 10 letters in the word AMALGAMATE can be arranged so that there is an M at the beginning, an M at the end and no As are together.

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• Question 6May/June 2024, paper 53Structured8 marks

  How many different arrangements are there of the 9 letters in the word RECORDERS?

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• Question 7May/June 2023, paper 53Structured9 marks

  Find the number of different arrangements of the 10 letters in the word CASABLANCA in which the two Cs are not together.

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• Question 7May/June 2025, paper 53Structured12 marks

  A set of friends consists of 7 men and 4 women. Three of the men are brothers: Ali, Ben and Charlie. Find the number of different arrangements of the 7 men in a line in which Ali and Ben do not stand next to each other.

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