Exercise 25 Page 809

We are told that there is a clearance box with a mix of dog toys. To know the probability of Johnda pulling out $2$ tug toys from that box, we need to divide the ways in which we can pull $2$ tug toys by the total number of ways in which we can pull $2$ items from the box. We are told that the box has $6$ balls, $5$ tug toys, $8$ rawhide chews, and $4$ chew toys. Let's add these items together to find how many items are in the box. Since the order in which the toys are pulled from the box does not matter, we will find the combinations of $n$ objects taken $r$ at a time. To find the ways in which we can pull $2$ items from the box, we will find the combinations of $23$ items taken $2$ at a time. There are $253$ ways in which we can pull $2$ items from the box. Now, to find the ways in which can pull $2$ tug toys, we will find the combinations of $5$ tug toys taken $2$ at a time. Let's do it! There are $10$ ways in which we can pull $2$ tug toys from the box. Finally, we can find the probability of pulling two tug toys from the box. Let's divide the ways in which we can pull two tug toys by the ways in which we can pull two items from the box. We can write this probability as a percent.