Final answer:
To find the number of possible outcomes for filling 3 distinct positions with 10 candidates, calculate the permutation 10! / (10-3)!, resulting in 720 different combinations.
Step-by-step explanation:
The question asks about the number of outcomes possible when filling 3 positions (President, Vice President, Manager) with 10 candidates. This is a problem of permutations where the order matters since each position is distinct. To determine the number of different outcomes, we calculate permutations using the formula P(n, k) = n! / (n-k)!, where n is the total number of items to pick from, and k is the number of items to pick.
Here, we have n = 10 candidates and k = 3 positions, so we calculate the permutation as follows: 10! / (10-3)! which is equivalent to 10 x 9 x 8 (since the factors from 7! on both numerator and denominator would cancel out). Therefore, the number of possible outcomes is 720.