How to Find 5 Factorial Video

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  • 0:04 Steps to Solve 5 Factorial
  • 0:40 Factorial Applications
  • 3:53 Lesson Summary
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Lesson Transcript
Instructor: Laura Pennington

Laura has taught collegiate mathematics and holds a master's degree in pure mathematics.

In this lesson, we learn how to find 5 factorial. We talk about different areas of mathematics in which factorials are used, and we also look at some applications that involve factorials and 5 factorial, specifically.

Steps to Solve 5 Factorial

In mathematics, an exclamation mark (!) is used to represent factorials. In general, n! represents n factorial, and it means that we want to multiply all the integers from n down to 1 together. The image shows this formula.


n factorial


We use the notation 5! to represent 5 factorial. To find 5 factorial, or 5!, simply use the formula; that is, multiply all the integers together from 5 down to 1.

5! = 5 * 4 * 3 * 2 * 1 = 120

When we use the formula to find 5!, we get 120. So, 5! = 120.

Factorial Applications

Factorials show up in many areas of mathematics, such as statistics, probability, calculus, and trigonometry. They're actually pretty well known for their use in combinatorics, which is a fancy name for counting techniques. Combinations and permutations make up a large part of combinatorics, and factorials are an essential part of both of these. Defined simply, combinations and permutations are arrangements of objects. In combinations, order does not matter, and in permutations, order does matter.

For example, if we're talking about 4-digit lock codes, the code 1234 is different than the code 4321, even though it contains the same numbers. Thus, order matters, and the lock codes are permutations of four digits. On the other hand, if we are putting a salad together with the ingredients lettuce, tomato, chicken, and onions, it is the same salad if we list the ingredients as tomato, lettuce, onions, and chicken. In this case, order does not matter, so the salad is a combination of four ingredients.

Factorials come into play when we're talking about formulas that give us the number of permutations or combinations of a number of objects. The images on your screen show some combination and permutation formulas. You don't have to memorize all of these formulas for the purpose of this lesson, but you should pause for a moment and take a closer look at how factorials are intricately used.


permutation formulas


combination formulas


Suppose we want to know how many ways there are for five people to finish a race. People can place first, second, third, fourth, or fifth. If the names of the competitors are Alex, Kennedy, Brock, Abrianna, and Peyton, consider them finishing in the following two orders:

Kennedy, Brock, Alex, Abrianna, Peyton

Brock, Alex, Kennedy, Peyton, Abrianna

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