Permutations

Permutations refer to the different ways in which a set of items can be arranged or ordered. When dealing with permutations, the order of the items matters. In other words, changing the order of the items results in a different permutation.

Formula for Permutations

The number of permutations of n items taken r at a time can be calculated using 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 "!" represents the factorial of a number.

Example

For example, if you have 5 different colored balls and you want to find the number of ways to arrange 3 of these balls in a row, you would use the permutation formula:

5P3 = 5! / (5 - 3)! = 5! / 2! = (5 × 4 × 3 × 2 × 1) / (2 × 1) = 60

So, there are 60 different ways to arrange 3 out of 5 colored balls in a row.

Study Guide for Permutations

1. Understand the concept of permutations and how they differ from combinations.
2. Learn the permutation formula and understand how to apply it to different scenarios.
3. Practice calculating permutations for various sets of items and different values of r.
4. Understand the concept of factorial and how it is used in the permutation formula.
5. Practice solving real-world problems involving permutations, such as arranging objects, seating arrangements, or selecting a committee.

Remember to pay attention to the order of the items when dealing with permutations, as changing the order results in a different permutation.