Permutations Part One

Hey guys! It's Bea! Today, we learned more new things about Permutations and I'm going to be writing a recap of the lesson that we covered.

First things first, what is a Permutation? 

          - A permutation of a set of distinct objects is an arrangement of objects into different orders. To permute a set of objects means to rearrange them.

We learned a formula that expresses the number of permutations chosen from a set of objects and that is:

where n is the total number of things to choose from and r is the amount you choose out of it

So this means, that n always has to be greater than r because it wouldn't make sense if you're, for example, choosing 6 (r) out of 3 (n). It is not possible. So n ≥ r.

There are two types of permutations: 

• Permutations without repetition: Number of permutations of n-things, taken 'r' at a time but 
  nothing can be repeated. You can use either the formula or the dash method to calculate.
• Permutations with repetitions: Number of permutations of n-things, taken 'r' at a time when 
  each thing can be repeated r-times. You cannot use the formula to calculate permutations where 
  repetitions are allowed. To calculate, use the dash method ( _____ · _____ )

Example 1: How many 3 letter words composed from the 26 letters in the alphabet are possible if...

a.) No repetitions are allowed?

For this case, we can use the Permutation formula.

Our values are:

n= 26 

r= 3

26P3 = 26! / (26-3)!

         = 26! / 23!

         = 26·25·24·23! / 23!

         = 26·25·24

         = 15,600 words

b.) Repetitions are allowed?

We cannot use the formula here so we're going to use the dash method.

_______ · ________ · ________

1st letter    2nd letter     3rd letter

= 26 · 26 · 26

= 17, 576 words

That's it!I hope this helps you guys understand it better! See you all in class tomorrow! :)

Bea Clarissa Guan