Answer:
we can fill the available spots of 120 different ways
Step-by-step explanation:
This is a combinatorics problem. We need to choose 3 people of 10
The formula for combinatorics is:

Where n is the total to choose from and k is the amount we're choosing.
Then:

And now solve:

We can cancel out 2 and 3, and we can develop the 7!:

Now we can cancel out 4, 5, 6, 7

Thus, the answer is: we can fill the available spots of 120 different ways