Permutations and FSP(fundamental principle of counting)

HELLO, everybody hope you're all doing WonderfullyExcelent, I know I am. Anyways, today in class we worked on PERMUTATIONS. An important thing to remember is:

A PERMUTATION IS AN ORDERED ARRANGEMENT OF OBJECTS WITHOUT REPETITION.

IT IS NOT A COMBINATION.

So, basically, a permutation is when you're calculating a series of things when the order matters. For example, your locker combination (which happens to be called the wrong thing) must be in the right order, therefore it is a permutation.

IT IS IMPORTANT THAT WE KNOW WHAT THE FUNDAMENTAL PRINCIPLE OF COUNTING IS. THE FUNDAMENTAL PRINCIPLE OF COUNTING IS THE IDEA BEHIND A FACTORIAL.

A FACTORIAL IS n!= (n+0)*(n-1) etc.

THE FUNDAMENTAL PRINCIPLE OF COUNTING BASICALLY MEANS

IF THERE IS m WAYS OF FINDING ONE THING AND n OF FINDING ANOTHER THING
m*n WILL TELL YOU THE WAY OF FINDING BOTH.

Now, we worked on a few problems that were permutations. One we worked on was:

How many 5 digit numbers can be made from the digits 0,1,2,3,4,5,6?

It is important to realize that having 0 included as one of the digits changed our results.
This was because 0 cannot be our first digit.

So this is how we solved it:

For digit 1 it could either be 1,2,3,4,5, or 6. This means we had 6 choices for the first digit.

For digit 2, you would think it just follow the general rule of a factorial and be n (which is 6)-1. However, it is 6 too. Why? Because for the first digit we only had 6 possible choices but there were 7 digits to choose from. This means that for digit 2, which can be 0, we have 6 digits to choose from and because it can be 0, unlike digit 1, we have 6 possibilities too.

For digits 3,4, and 5, we just follow the factorial rule.

SOMETHING IMPORTANT TO REMEMBER!

0!=1

We also learned a formula today for permutation equations. This formula is called the "Pick" formula and it looks like this:

nP r= n!/(n-r)!

Now to show you how this equation can be applied....

Lets say you have 2 people and 22 seats. How many different ways can people sit?

Well....

n= The number of objects to be chosen from. So, in this case the number of chairs, 22.

r= The number of objects to be arranged. In this case the number of people, 2.

Now plug this into the equation like this:

P= 22!/(22-2)!

P= 22!/20!

P= 22*21

P= 462

And Bam, Peanut Butter and Jam! You've got the solution :).

So, in closing, you should know what a permutation is. You should know how and why a combination and permutation are different. You should also know the new equation and how to use it. Finally, remember that 0!=1.

I now leave you with a fun problem. If your bank card has 16 digits, what is the chance that someone will guess it right? And if your pin number has 4 digits, what is the chance that someone will guess that right? Finally, what is the chance that someone will guess your pin and your bank card number right?

Well, by everyone. Hope you found this helpful. Take care and go out and commit random acts of WondefullyExcelentness :).