Watch the Permutations video to review what you have learned about solving permutation problems.

 

It is common with permutation problems that conditions are given to some of the objects. The remainder of this lesson explores the more common conditions that arise.

The following are examples of AND conditions . To solve, you multiply the numbers of ways each task can occur in the problem.

  • Repetition - Object(s) are used more than once in the arrangement.

  • Placement - Object(s) are assigned to a particular place in the arrangement.

  • Grouping - Objects are required to be together in the arrangement.

All OR conditions involve cases. To solve, you add the number of ways each task can occur.

  • Cases - Arrangements are determined according to given constraints.

The following is a general strategy to follow when solving a permutation problem that involves conditions.

  1. Determine the appropriate formula ; .

  2. Use the formula to permute each task in the arrangement.

  3. Based on the condition, multiply or add the permutations of each task.

Examples 5 and 6 show you how to implement this strategy.