At the beginning of summer you have 6 books to read In how many orders can you read the book Is this a permutation or combination?

You have a choice of 6 books for the first book, leaving a choice of 5 for the second, for each of the choice of first book, and so on until a reading order list has been made. This can be done in 6 x 5 x 4 x 3 x 2 x 1 = 720 ways.

This is a permutation as the order of choice matters.

A combination is where the order doesn't matter, ie a group has been selected, for example: You have a reading list of 6 books, but only need to read 4 of them over the summer, borrowing them from a library; how many groups of 4 books can you choose from the reading list and take home from the library.

In this case, you can select (6 x 5 x 4 x 3) ÷ (4 x 3 x 2 x 1) = 15 different groups of 4 books from your reading list of 6 (and when you have your group it can be ordered in 4 x 3 x 2 x1 = 24 different ways for reading).