The situation that represents a combination is option c. choosing a committee of three people from a group of 10.
In a combination, the order in which the objects are selected does not matter, and the formula for the number of combinations is:
n C r = n! / (r! * (n-r)!)
where n is the total number of objects, and r is the number of objects being chosen.
Option a, Seven people running for chair and vice-chair, represents a permutation, not a combination, because the order in which the people are chosen matters.
Option b, First and second place in a race, also represents a permutation, not a combination, because the order in which the runners finish matters.
Option d, Five people in line to buy tickets, does not involve choosing objects from a larger set of objects, so it does not represent a combination or permutation.
Therefore, the correct response is:
c. choosing a committee of three people from a group of 10.