Permutations and combinations — AS & A Level Mathematics (9709) questions by topic
Counting arrangements of letters in words such as REGENERATE and RECORDERS, and arranging the letters of KANGAROO or HAPPINESS under conditions like two identical letters staying together or apart, are typical of the 27 permutations and combinations questions from 2023 to 2025, worth 4 to 12 marks.
Find and write lead the command words, with comment occasionally asking you to justify why a count method is valid. Because repeated letters and grouping conditions are the usual source of error, submit each arrangement calculation for instant marking, so a double-counted or under-counted case is caught the moment it happens rather than after the whole answer is built on it.
May–June 2025, Paper 51
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.
Answer this question and get it marked →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. Find the number of different ways in…
Answer this question and get it marked →May–June 2025, Paper 52
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.
Answer this question and get it marked →May–June 2025, Paper 53
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…
Answer this question and get it marked →May–June 2025, Paper 55
A darts club has 12 members made up of 7 men and 5 women. Every Monday, a team of 4 is chosen at random to represent the club in a competition. Find the probability that, on a…
Answer this question and get it marked →May–June 2025, Paper 61
At an entertainment centre, the cost for using a particular video game is $0.40 per minute. The number of minutes for which people use the video game has mean 15 and variance 9.…
Answer this question and get it marked →May–June 2025, Paper 63
In Urberia, the masses, in kilograms, of men have the distribution N(70.3, 5.9^2). A certain footbridge in Urberia can take a maximum safe load of 1500 kg. When n men stand on the…
Answer this question and get it marked →May–June 2025, Paper 65
Candidates for a certain diploma take two tests. Their marks for the first test and the second test are modelled by the independent variables with distributions N(38.1, 3.8^2) and…
Answer this question and get it marked →May–June 2024, Paper 51
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?
Answer this question and get it marked →May–June 2024, Paper 52
How many different arrangements are there of the 10 letters in the word REGENERATE?
Answer this question and get it marked →May–June 2024, Paper 53
How many different arrangements are there of the 9 letters in the word RECORDERS?
Answer this question and get it marked →May–June 2024, Paper 62
A random variable X has the distribution N(10, 12). Two independent values of X, denoted by X1 and X2, are chosen at random. Write down the value of P(X1 X2).
Answer this question and get it marked →October–November 2024, Paper 51
How many different arrangements are there of the 9 letters in the word INTELLECT in which the two Ts are together?
Answer this question and get it marked →October–November 2024, Paper 52
Find the number of different arrangements of the 9 letters in the word ALGEBRAIC.
Answer this question and get it marked →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…
Answer this question and get it marked →October–November 2024, Paper 53
Find the number of different arrangements of the 9 letters in the word HAPPINESS.
Answer this question and get it marked →May–June 2023, Paper 51
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.
Answer this question and get it marked →Find the number of different arrangements of the 8 letters in the word COCOONED.
Answer this question and get it marked →May–June 2023, Paper 52
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…
Answer this question and get it marked →May–June 2023, Paper 53
Find the number of different arrangements of the 10 letters in the word CASABLANCA in which the two Cs are not together.
Answer this question and get it marked →May–June 2023, Paper 62
Two random variables X and Y have the independent distributions N(7, 3) and N(6, 2) respectively. A random value of each variable is taken. Find the probability that the two…
Answer this question and get it marked →October–November 2023, Paper 51
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…
Answer this question and get it marked →October–November 2023, Paper 52
Find the number of different arrangements of the 9 letters in the word ANDROMEDA in which no consonant is next to another consonant. (The letters D, M, N and R are consonants and…
Answer this question and get it marked →October–November 2023, Paper 53
Jai and his wife Kaz are having a party. Jai has invited five friends and each friend will bring his wife, making 12 people in total. At the beginning of the party, the 12 people…
Answer this question and get it marked →October–November 2023, Paper 61
The masses, in kilograms, of chemicals A and B produced per day by a factory are modelled by the independent random variables X and Y respectively, where X ~ N(10.3, 5.76) and Y ~…
Answer this question and get it marked →October–November 2023, Paper 62
A factory makes loaves of bread in batches. One batch of loaves contains X kilograms of dried yeast and Y kilograms of flour, where X and Y have the independent distributions…
Answer this question and get it marked →October–November 2023, Paper 63
The masses, in kilograms, of chemicals A and B produced per day by a factory are modelled by the independent random variables X and Y respectively, where X ~ N(10.3, 5.76) and Y ~…
Answer this question and get it marked →Other AS & A Level Mathematics topics
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- Algebra, logarithmic and exponential functions (87)
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- Series (37)
- Integration (33)
- Kinematics (33)
- The normal distribution (32)
- Energy, work and power (31)
- The Poisson distribution (31)
- Complex numbers (28)
- Sampling and estimation (28)
- Representation of data (23)