# Radio stations in a certain country use a sequence of 4 or 5

Last updated: 8/8/2022

Radio stations in a certain country use a sequence of 4 or 5 letters as their station identification call letters. The first letter must be W, P, A, or Q. Assume there are no restrictions on the remaining letters, and repetition is allowed. a) How many 4-letter station identifications are possible? b) How many 5-letter station identifications are possible? c) How many total station identifications are possible? d) The identification for a randomly-chosen radio station is 4 letters in length. What is the probability that all four letters are different? a) Set up the expression that would be used to calculate the number of possible 4-letter station identifications. The expression is ___ (Do not simplify.) There are ___ possible 4-letter station identifications. (Simplify your answer.) b) There are ___ possible 5-letter station identifications. (Simplify your answer.) c) The total number of possible station identifications is ___ (Simplify your answer.) d) If the identification for a randomly-chosen radio station is 4 letters in length, then the probability that all four letters are different is ___ (Round to three decimal places as needed.)