Answer: 720 ways
Explanation:
We have a total of 10 numbers and 3 selections:
When Alice chooses, she has 10 possible numbers to choose.
When Bob chooses, he has 9 possible numbers to choose (because one has already ben selected)
When Carrie chooses, she has 8 possible numbers to choose (because two numbers had already been selected)
The number of combinations is equal to the product of the number of options for each selection:
C = 10*9*8 = 90*8 = 720