A small number of finches are removed randomly from the wild and placed in a protected
bird area. They are given as much food as they need and have plenty of space. Why
would natural selection not occur in this population?
-The population has not reached carrying capacity.

Natural selection can cause microevolution (change in allele frequencies), with fitness-increasing alleles becoming more common in the population.

Organisms with heritable (genetically determined) features that help them survive and reproduce in a particular environment tend to leave more offspring than their peers. If this continues over generations, the heritable features that aid survival and reproduction will become more and more common in the population. The population will not only evolve (change in its genetic makeup and inherited traits), but will evolve in such a way that it becomes adapted, or better-suited, to its environment.

Hope this helps...