Factorials and Permutations Examples

What are all the permutations of the numbers 1, 2, and 3?

1, 2, 3 

1, 3, 2 

2, 1, 3

 2, 3, 1 

3, 1, 2 

3, 2, 1

How many ways can we choose 3 books from 2 books, with repetition allowed?

We have two choices for the first book, two for the second, and two for the third:

How many ways can we choose 2 books from 3 books, with repetition allowed?

We have 3 choices for the first book, and 3 choices for the second: