An isolated population of prairie dogs has longer than average teeth. as a result they can eat more grass with less effort and are better able to survive. the mutations(s) that resulted in longer teeth:

(a) allowed the teeth to grow longer over several generations until they reached an optimal length for eating grass.
(b) arose in many members of the population at the same time.
(c) happened by chance.
(d) occurred because the prairie dogs needed to be more efficient at eating grass to survive and reproduce.
(e) would only occur in a prairie dog population that eats grass and would not occur in a population that lives on seeds.

c) happened by chance

Explanation:

d and e answers are not correct:

mutations won't happen because of an environmental necessity, like being more efficient at eating grass, nor because a specific diet requirement, like eating seeds or grass. Mutations could happen if the organisms have the genetic pool to express a specific mutation dealing with a phenoypic character like longer teeth. If the organism doesn't have the genetic pool for developing longer teeth it will never have this feature, even if it keeps eating grass all its life.

A is not correct:

The mutation allowed the teeth to grow longer and to pass this feature to the next generation, but there is nothing that can predict an optimal length for eating grass to make them stop growing. Mutations are not a synonym of optimal features or benefit.

B is not correct:

It could happen that longer teeth arose in many members of the population, but we cannot say that it arose at the same time.