Cambridge O Level Additional Mathematics · Syllabus 4037 · Permutations and Combinations
Relationship Between Permutations and Combinations
What is Relationship Between Permutations and Combinations?
Two identities connect the two counting formulas. The first, n P r equals r factorial multiplied by n C r, holds because any ordered arrangement of r objects can be built in two stages: first select which r objects are used, then arrange those r objects among themselves in r factorial ways. The second, n C r equals n C (n minus r), holds because deciding which r objects go in simultaneously decides which n minus r objects are left out, so the two counts describe the same set of outcomes. The first identity is used to check an answer and the second to shorten a calculation or to solve an equation such as n C 4 equals n C 7.
This definition is part of the Permutations and Combinations chapter in Cambridge O Level Additional Mathematics.