Using Factorial Notations and Permutations

Today we went over on how to use factorial notations and permutations. So if anyone else missed the class here it is..

Factorial Notations
We learned that the symbol "!" can be used to multiply a number down to 1. So if we want to multiply 6 * 5 * 4 * 3 * 2 * 1 = 720, we can simply use "!" to make it easier to multiply. So it would look like this: 6!.

Examples for using factorial notations
So this is what we do:

So in the calculator it should look like this:

10!/(7!3!)*(1/2)^7*(1/2)^3

(and make sure that you put brackets in or it will make no sense at all)

When we equal it, it becomes 0.117 which is 11.7%.

Using Permutations
We use permutations to see how many ways can object be arranged and to do that we use the formula:

nPr = n!/(n-r)!

n is the number of objects available to be arranged.
r is the number of objects that are being arranged.

Examples using permutations

If we had 10 students in our class and we wanted to find how many ways can we change seating plans, there would be 3628800 ways to do it. This is how i know:

But what if there were 5 extra seats? We would do that same thing we did but we'd switch the "n's" to 15 so theres 15 vacant seats. So it would look like this: