Permutations
Permutations tests the fundamental principle of counting, arrangements with and without repetition, restricted arrangements, and circular permutations. The exam expects you to decide whether order matters before calculating.
Core rules
If a task has m choices followed by n choices, the total is m×n. The number of arrangements of r distinct objects from n is nPr=n!/(n−r)!. If some objects are identical, divide by the factorials of repetition counts: n!/(p!q!…). Circular arrangements of n distinct objects are (n−1)!; for a necklace where clockwise and anticlockwise are the same, divide by 2. Restrictions are handled by fixing positions first or by subtracting forbidden arrangements from the total.
Worked example
Find the number of distinct arrangements of the letters of LEVEL. There are 5 letters, with L repeated twice and E repeated twice. Total arrangements=5!/(2!2!)=120/4=30. The V is the only single letter and does not require division.
Traps
Use permutations only when order matters; selections use combinations. Do not divide by a factorial unless the repeated objects are truly identical. In circular problems, fix one person to remove rotational symmetry. For numbers, handle the leading-zero restriction separately. 'At least one' is often easier by complement, but check whether the complement is allowed.