Question

peahens prefer to mate with peacocks that have the brightest and largest tail displays. the peacocks tail is a disadvantage to the males, because it is large and cumbersome and hinders them from escaping from predators. given these facts, why isnt the peacocks tail selected against by natural selection?
peacocks lack the mutations to allow selection to work
only a few peacocks have large tail displays
in spite of the disadvantage, peacocks with larger tails leave more offspring
it is selected against, but because a peahen gives birth to so many males, the population is not greatly affected
peacocks do not reproduce sexually

Explanation:

Natural selection favors traits that increase an organism's reproductive success. Peacocks with larger tails may have a survival disadvantage (e.g., harder to escape predators), but if peahens prefer them for mating, they will have more offspring. Over time, genes for larger tails are passed on more frequently. Even with a survival cost, the reproductive benefit can outweigh it.

Answer:

in spite of the disadvantage, peacocks with larger tails leave more offspring