What is the FACT function?

The FACT function returns the factorial of a number.

What is the factorial of a number?

The factorial of a number n is the product of all positive integers less than or equal to n, and is represented by n!

The factorial of a number n is defined as:

n! = n * (n-1) * (n-2) * ... * 3 * 2 * 1

In other words, the factorial of a number n is the product of all positive integers less than or equal to n.

Some examples:

1! = 1
2! = 2 * 1 = 2
3! = 3 * 2 * 1 = 6
4! = 4 * 3 * 2 * 1 = 24
5! = 5 * 4 * 3 * 2 * 1 = 120
0! = 1

The factorial function grows very quickly as n increases. Factorials are useful in combinatorics for counting permutations and combinations.

How to calculate combinations using factorials?

The formula for combinations is:

C(n, r) = n! / (r! * (n-r)!)

Where:

n = Total number of objects
r = Size of the subset we choose

For example, say we have 5 fruits: apple, banana, orange, mango and peach. We want to calculate how many combinations of 3 fruits there are from this set of 5 fruits.

n = 5 (total fruits) r = 3 (size of subset)

C(5, 3) = 5! / (3! * (5-3)!) = 120 / (6 * 2) = 10

How to calculate permutations using factorials?

For example, ordering 3 letters out of the alphabet.

The formula for permutations is:

P(n, r) = n! / (n - r)!

Where:

n = Total number of objects
r = Number of objects being arranged

For example, say we want to find how many ways we can arrange 3 letters from the alphabet.

n = 26 (total letters) r = 3 (letters we are arranging)

P(26, 3) = 26! / (26 - 3)! = 26! / 23! = 15600

What are permutations?

A permutation is a way of arranging a set of elements in a specific order. For example, if you have three letters A, B, and C, you can arrange them in six different ways: ABC, ACB, BAC, BCA, CAB, and CBA.

Each of these arrangements is called a permutation of the three letters. The order of the objects matters in a permutation, so ABC and BAC are considered different permutations.
The PERMUT and PERMUTATIONA functions are in the Statistical category

What are combinations?

A combination is a way of selecting items from a collection where the order of selection does not matter.

For example, if you have three fruits, say an apple, an orange, and a pear. There are three combinations of two that can be drawn from this set:

• apple and a pear
• apple and an orange
• pear and an orange

The COMBIN and COMBINA functions are in the Math and trigonometry category.

Formula in cell C3:

Example, 3! = 3*2*1 = 6

1. FACT Function Syntax

FACT(number)

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2. FACT Function Arguments

If number is not an integer, it is truncated.

Returns an error if the number argument is a text value.

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3. FACT Function example

The FACT function is useful if you want to calculate the number of permutations of a given set of elements.

The following set has three elements: [A, B, C].

3! = 3*2*1 = 6. You can rearrange [A, B, C] in six different permutations.

1, [A, B, C]
2, [A, C, B]
3, [B, A, C]
4, [B, C, A]
5, [C, A, B]
6, [C, B, A]

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'FACT' function examples

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Functions in 'Math and trigonometry' category

The FACT function function is one of many functions in the 'Math and trigonometry' category.

Excel categories

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