Final answer:
To determine the number of different combinations for a president and vice-president among 11 people, calculate the permutations for 2 distinct positions from the 11 candidates, which is 11 × 10 = 110.
Step-by-step explanation:
The question relates to calculating the number of different combinations that can be made among 11 people when electing a president and a vice-president. Since the president and vice-president are distinct positions, we're looking for permutations, not combinations. The first step is to select a president from the 11 candidates, which can be done in 11 ways. After choosing a president, we then have 10 remaining candidates for the vice-president position, which gives us 10 ways to make this selection. The total number of different permutations is the product of these selections.
The formula for permutations when selecting r objects from a set of n objects is n! / (n-r)! where ! denotes factorial. For our problem, we're selecting 2 positions (president and vice president) from 11 people, so we use the formula 11! / (11-2)!, which simplifies to 11 × 10 = 110 permutations.
Therefore, the number of different combinations of president and vice-president among 11 people is 110.