How does n factorial work

Change ringing was a part of the musical performance where the musicians would ring multiple tuned bells. And it was in the year , when a mathematician from France, Christian Kramp, came up with the symbol for factorial: n! The study of factorials is at the root of several topics in mathematics, such as the number theory, algebra, geometry, probability, statistics, graph theory, and discrete mathematics, etc. The factorial of a number is the function that multiplies the number by every natural number below it.

Symbolically, factorial can be represented as "! So, n factorial is the product of the first n natural numbers and is represented as n! For example, 4 factorial, that is, 4! Observe the numbers and their factorial values given in the following table. To find the factorial of a number, multiply the number with the factorial value of the previous number.

For example, to know the value of 6! For 7! This means that the factorial of any number is, the given number, multiplied by the factorial of the previous number. Zero factorial or Factorial of 0 is interesting, and its value is equal to 1, i. Let's start with 3! And from here on down all integer factorials are undefined. So, negative integer factorials are undefined. Now, permutation is an ordered arrangement of outcomes and it can be calculated with the formula:.

Combination is a grouping of outcomes in which the order does not matter. It can be calculated with the formula:. In how many ways can the prizes be distributed? This is permutation because here the order matters. This is a combination because here the order does not matter. The factorial of n is denoted by n! Examples: 4! We usually say for example 4! Example: 9! Try to calculate 10! Example: how many ways can we arrange letters without repeating? Just one way, an empty space: So 0!

Example: How many different ways can 7 people come 1 st , 2 nd and 3 rd? The list is quite long, if the 7 people are called a,b,c,d,e,f and g then the list includes: abc, abd, abe, abf, abg, acb, acd, ace, acf, Example: What is !

Using our knowledge from the previous example we can jump straight to this: ! Related: 20 Jobs for Mathematics Degree Holders. You can follow these steps to solve for a factorial:.

Determine the number you are finding the factorial of. A factorial has a positive integer and an exclamation point. For example, if you want to find the factorial for the number eight, mathematically, it would look like:.

Using the factorial formula, you can write out the sequence of numbers that you'll multiply. This includes the number you are finding the factorial for, the number eight in this example, and all the numbers descending sequentially from it down to one. Mathematically, it would like this:. Once you have the sequence of numbers written down, you can multiply them together.

Mathematically, it looks like this:. You can also compute a factorial using a scientific calculator. The calculator should have a button with the " x!

Type in the number you want to find the factorial for, in this case, the number eight, and then push the " x! The calculator should give you the same answer, 40, Problem: How many ways can you arrange the letters in the word "company" without repeating them? For this problem, count the number of letters in the word "company" to find there are six letters.

Then, find the factorial of the number six either by hand or by using a scientific calculator. If you solve the problem by hand, it should look like this:. Now you know that the maximum number of ways, you can arrange the letters in the word "company" with no repeats is Problem: What combinations can you make with the colors red, blue and green? For this problem, find the factorial for the number three because there are three colors, then list the different combinations.

If you solve this problem by hand, it should look like this:. Problem: Find the factorial for the number While it's possible to solve this problem by hand, it could take a long time because 15 is a large number. It's easier to use a scientific calculator.