Permutations of a Set Formula
The number of permutations of a set is given by factorial, where is the number of elements in the set. A permutation is a unique ordering of the elements where order matters.
Formula Terms
| Expression | Description |
|---|---|
| Number of elements in the set | |
| Factorial operator |
To calculate the number of permutations of a set, take the factorial of the number of elements in the set. For example, the number of permutations for the set is given by the formula below. Since there are elements in the set .
There are possible permutations of the set . The possible permutations are shown below.
- (🍄, 🌿, 🐟)
- (🍄, 🐟, 🌿)
- (🌿, 🍄, 🐟)
- (🌿, 🐟, 🍄)
- (🐟, 🍄, 🌿)
- (🐟, 🌿, 🍄)
The permutation formula calculates the possible permutations of r elements out of a group of n elements where order does matter.
The combination formula calculates the possible combinations of r elements out of a group of n elements where order does not matter.