# Factorials!

Actually, that would be Factorials*Factorial*Factoria*Factori*Factor*Facto*Fact*Fac*Fa*F. I think.

So, anyways, in math class, have you ever seen an exclamation point next to the number and been like ‘what is that’?

Yup, me too. But I finally found out!

A factorial number, like 6! is basically the consecutive multiplication of all whole numbers including and below the factorial number. For example, 6! is not being extremely excited about the number 6, it is…

6*5*4*3*2*1which equals 30*4*6 or 30*24 or 720.

Factorials are useful in long equations, and something called ‘combinarics.’

Now, I’m handing it over to Tiffany for some more elaboration on factorials!

-Eleanor

Factorials are very useful for daily life. Permutation relates to the act of rearranging all the members of a set into some order. The permutations of n are n!. For example, if you want to know how many ways you can arrange 10 magnets in a straight line, the answer is 10! = 3,628,800. Wow! (I almost put the exclamation after the answer! 😨) Also, factorials are very useful in finding out how many combinations of 3 flavors of ice creams you have, if there are 10 flavors and there is no repetition and order does not matter. It can be found with this formula:

Where that first symbol means “there are n things to choose from, and we will pick k of them.” Then the rest is, well, factorials.

Now to a different question: What is 0!? (That looks weird!) 0! = 1, according to the convention for empty products, which says that multiplying no factors is equal to the multiplicative identity 1. 1!=1, also! Watch out, though, not to over do anything like this- it can get dangerous super fast. 20! = 2432902008176640000, so, you probably can’t imagine what 100! looks like…

Happy Factorials!

-Tiffany