At a certain company, passwords must be from 3-5 symbols long and composed of the 26 letters of the alphabet, the ten digits 0-9, and the 14 symbols !,@,#,$,%,ˆ,&, ∗,(,),-,+,{, and }.
a. How many passwords are possible if repetition of symbols is allowed?
b. How many passwords contain no repeated symbols?
c. How many passwords have at least one repeated symbol?
d. What is the probability that a password chosen at random has at least one repeated symbol?