)(25 points) I write each of the letters 'P', 'R', 'I', 'D', 'E' on separate pieces of paper and put these into a hat. I close my eyes and begin picking the pieces of paper from the hat and reading off the letters written on the pieces of paper.

a. (5 points) If I do NOT put the pieces of paper back into the hat after each choice and pick 5 pieces of paper what is the probability that the letters come out exactly in the order 'PRIDE'?

b. (5 points) If I put the pieces of paper back into the hat after each choice and pick 5 pieces of paper, then what is the probability that the letters come out exactly in the order 'PRIDE'?

c. (5 points) If I put the pieces of paper back into the hat after each choice and pick 5 pieces of paper, then what is the probability that the letters picked can be rearranged to spell 'PRIDE'?

d. (5 points) If I put the pieces of paper back into the hat after each choice and pick 5 pieces of paper, then what is the probability that there are exactly two 'P' letters among the 5 letters picked?

e. (5 points) If I put the pieces of paper back into the hat after each choice and continue to pick letters until the first 'P' occurs, what is the probability the first 'P' occurs as the 4th letter picked?