Suppose we randomly select a permutation of the letters in PEACEPIPE. Let E be the event that I precedes C. Let F be the event that I immediately precedes an E. What are the probabilities p(E), p(F) and p(E|F)? Express your answers as fractions with the smallest positive integer denominators possible. Explain your answers.

Aamir wants to raise some money for a charity by running a lottery. For a fixed contribution of a yet to be determined amount of X dollars, he lets a contributor select a string of three octal digits (Recall that an octal digit is one of {0, 1, 2, 3, 4, 5, 6, 7}). Anyone who selects the randomly selected winning string wins three hundred dollars. Anyone who selects a string that matches the winning string in exactly two places wins fifteen dollars. What should X be if Aamir wants to raise an average of X 2 dollars per contributor? Explain your answer.