Five friends, named Ali, Bob, Charlie, Daniel, and Ebony, each pick a letter from the alphabet on their own (i.e., independently), with all possible outcomes equally likely. For instance, they might pick (starting with Ali's choice) "M,D,P,Z,P."
a. What is the probability that they choose 5 distinct letters?
b. What is the probability that they choose 5 distinct letters and that the letters are in increasing alphabetic order starting from Ali's choice and ending at Ebony's choice? For instance, starting with Ali's choice, "D,H,P,T,X" would be such an alphabetical ordering.