Cambridge IGCSE Additional Mathematics · Syllabus 0606 · Permutations and Combinations
Mutually Exclusive Cases
What is Mutually Exclusive Cases?
A way of splitting a counting problem into separate situations such that every outcome belongs to exactly one of them, so that their counts may be added without double counting. Cases are mutually exclusive when no outcome can satisfy two of them at once, which is guaranteed if they are defined by the exact value of some quantity, such as the exact number of girls on a team. Within a single case the successive independent choices are multiplied, because they are stages of building one outcome, while the totals for separate cases are added, because the cases are alternatives. Overlapping cases inflate the answer invisibly, since the excess never appears as an obviously impossible value.
This definition is part of the Permutations and Combinations chapter in Cambridge IGCSE Additional Mathematics.