Given 5Pr  60 , solve for r .

The given expression is a permutation, denoted as nPr, where n is the total number of items, and r is the number of items to choose. The formula for permutations is:

nPr = n! / (n-r)!

where "!" denotes factorial, which is the product of all positive integers up to that number.

In this case, we have 5Pr = 60. We need to solve for r.

Let's start by expanding 5!:

5! = 5 * 4 * 3 * 2 * 1 = 120

So, the equation becomes:

120 / (5-r)! = 60

Solving for (5-r)! gives us:

(5-r)! = 120 / 60 = 2

Now, we need to find a factorial that equals 2. The only option is 2!, since 2! = 2 * 1 = 2.

So, we have:

2! = (5-r)!

This implies that 5-r = 2.

Solving for r gives us:

r = 5 - 2 = 3

So, r = 3 is the solution.