Permutations

Permutation is the arrangement of items in a particular order. In mathematics, it refers to the different ways in which a set of items can be arranged in a specific order. The number of permutations of a set of items can be calculated using the permutation formula.

Permutation Formula

The number of permutations of n items taken r at a time is given by the formula:

nPr = n! / (n - r)!

Where n is the total number of items, r is the number of items taken at a time, and ! denotes factorial, which means the product of all positive integers less than or equal to n.

Example

Suppose we have a set of 5 letters: A, B, C, D, and E. We want to find the number of different ways these letters can be arranged in a 3-letter sequence. Using the permutation formula, we can calculate this as:

5P3 = 5! / (5-3)! = 5x4x3 / 2x1 = 60

Study Guide

To understand permutations better, here are some key points to remember:

1. Permutation refers to the arrangement of items in a specific order.
2. The permutation formula is nPr = n! / (n - r)!, where n is the total number of items and r is the number of items taken at a time.
3. Factorial (!) denotes the product of all positive integers less than or equal to n.
4. Practice calculating permutations using different sets of items and varying the number of items taken at a time.

Understanding permutations is important in various mathematical and real-life scenarios, such as arranging objects, scheduling tasks, and solving combinatorial problems.