Permutations and combinations — IGCSE Mathematics - Additional (0606) questions by topic
Permutations and combinations questions ask you to find an unknown value of n from an equation combining permutation notation, work out how many five-digit numbers greater than 50,000 can be formed from a set of digits, show algebraically that a difference of combination terms simplifies to another combination term, and find arrangements of club members standing together in groups. Find and show are the only command words tested, each requiring precise use of permutation or combination formulae rather than listing outcomes.
Marks run from 4 to 8 across the 5 real questions here, all from 2025 papers. Because a single misapplied formula, such as using a permutation where a combination was needed, produces a plausible but wrong answer, submit your workings for instant marking to check the correct notation was used from the first line.
May–June 2025, Paper 11
In this question n ≥ 6. Use an algebraic method to show that (n choose 5) − (n−1 choose 5) can be written as (n−1 choose 4). [In standard notation: nC5 − (n−1)C5 = (n−1)C4.]
Answer this question and get it marked →May–June 2025, Paper 21
A sports club has the following members: 5 runners, 4 swimmers, 3 gymnasts. These members stand in a straight line. Find the number of ways that this can be done when all the…
Answer this question and get it marked →May–June 2025, Paper 22
A 4-digit number is to be formed using the digits 0, 2, 4, 5, 6 and 8. The 4-digit number must not start with 0. Any digit may be used at most once in the 4-digit number. Find how…
Answer this question and get it marked →May–June 2025, Paper 23
Five of the digits 1 2 3 4 5 6 7 8 9 are used to make a 5-digit number. Find how many ways this can be done when the 5-digit number is greater than 50 000.
Answer this question and get it marked →Given that ((n+1)P5) / 437 = (nP3), use an algebraic method to find the value of n.
Answer this question and get it marked →Other IGCSE Mathematics - Additional topics
- Differentiation (9)
- Series (8)
- Functions (5)
- Logarithmic and exponential functions (5)
- Trigonometry (5)
- Integration (5)