Ex: You have five books and you are going to put three on a bookshelf. How many different ways can the books be ordered on the bookshelf? Counting Rule 5: Combinations:The number of ways of selecting X objects from n objects, irrespective of order, is (}_{n)C_(x)=(n!)/(X!(n-X)!)

To find the number of different ways to arrange three books out of five on a bookshelf, we can use the formula for combinations: In this case, n = 5 (the total number of books) and x = 3 (the number of books we want to arrange on the bookshelf).Plugging in the values, we get: Simplifying the expression, we have: Calculating the factorials, we get: Simplifying further, we have: Finally, calculating the expression, we get: Therefore, there are 10 different ways to arrange three books out of five on a bookshelf.