PERMUT function

The PERMUT function in Excel is used to calculate the number of permutations for a given number of objects. A permutation is an arrangement of objects where the order matters. This function is useful when you want to find out how many ways you can arrange a subset of objects from a larger set.

Syntax:

PERMUT(number, number_chosen)

Arguments:

• number: Required. The total number of items (objects) in the set.
• number_chosen: Required. The number of items to choose and arrange from the total set.

Output:

The function returns the number of permutations possible when choosing number_chosen items from a set of number items.

Formula:

The general formula for permutations is:

$$P(n, k) = \frac{n!}{(n – k)!}$$

Where:

• $n!$ is the factorial of $n$,
• $(n – k)!$ is the factorial of $(n – k)$.

Example 1: Finding the Number of Permutations

Suppose you have a set of 10 objects and you want to find how many ways you can arrange 3 objects from that set.

Use the formula:

=PERMUT(10, 3)

This will return 720, meaning there are 720 possible ways to arrange 3 objects from a set of 10.

Example 2: Finding Permutations for a Smaller Set

If you have 5 objects and want to find how many ways you can arrange 2 objects, use the formula:

=PERMUT(5, 2)

This will return 20, meaning there are 20 possible ways to arrange 2 objects from a set of 5.

Key Points:

• PERMUT calculates permutations where the order of the items matters.
• The number of possible permutations is larger than combinations because the order of the items is considered.
• The number must be greater than or equal to number_chosen; otherwise, Excel will return an error.

Use Cases:

• Statistics: Calculate permutations when order matters, such as in ranking or ordering tasks.
• Combinatorics: Solve problems where you need to arrange or select items from a set.
• Games: Determine the number of ways to arrange or order cards, people, or objects.

Notes:

• If number_chosen is greater than number, Excel will return an error (#NUM!).
• The PERMUT function is specifically designed for cases where the order of selection is important. If the order does not matter, use the COMBIN function for combinations instead.