has 10 basketballs, each of a different colour. She only has time to shoot 5 hoops before going to bed. How many different arrangements can the balls be thrown into the hoops? 120 3,628800 30,240 252

## Step 1: Understanding the Problem<br />### The problem asks for the number of different arrangements of 10 distinct basketballs when choosing 5. This is a permutation problem since the order matters.<br /><br />## Step 2: Applying the Permutation Formula<br />### The formula for permutations is $_nP_r = \frac{n!}{(n-r)!}$, where $n$ is the total number of items and $r$ is the number of items chosen. In this case, $n = 10$ and $r = 5$. So, we have $_{10}P_5 = \frac{10!}{(10-5)!} = \frac{10!}{5!} = 10 \times 9 \times 8 \times 7 \times 6 = 30240$.