Restricted Arrangement

What is Restricted Arrangement?

An arrangement problem in which some condition limits where objects may go or which objects may be used, for example that a particular person must be included, must be left out, or must occupy a stated position. The standard method is to satisfy the restriction first, counting the number of ways of making the restricted choice, and then to fill the remaining positions from the objects that are still available using an ordinary permutation. The two counts are multiplied because the choices are consecutive and independent. A restriction can only reduce the unrestricted count, which provides a check on the answer.

This definition is part of the Permutations and Combinations chapter in Cambridge O Level Additional Mathematics.

Concepts related to Restricted Arrangement

• restriction first
• product rule
• complementary counting