The number of ways to pick 3 astronauts from 10 candidates can be found using the combination formula, which is:
nCk = n! / (k!(n-k)!)
where n is the total number of candidates, k is the number of candidates to be chosen, and "!" denotes the factorial function.
In this case, we want to choose 3 astronauts from a pool of 10 candidates, so we can plug these values into the formula:
10C3 = 10! / (3!(10-3)!)
= (10 x 9 x 8) / (3 x 2 x 1)
= 120
Therefore, there are 120 ways to pick 3 astronauts to go to the moon out of 10 candidates.