Question

In: Statistics and Probability

Radio stations in a certain country use a sequence of 3 or 4 letters as their...

Radio stations in a certain country use a sequence of 3 or 4 letters as their station identification call letters. The first letter must be Upper W comma Upper K comma Upper B comma Upper Q comma or Upper R. Assume there are no restrictions on the remaining letters, and repetition is allowed. a) How many 3-letter station identifications are possible? b) How many 4-letter station identifications are possible? c) How many total station identifications are possible? d) The identification for a randomly-chosen radio station is 3 letters in length. What is the probability that all three letters are different?

Expert Solution

Initially the constraint on 1st letter is as follows

It must be W,K,B,Q,R

Rest the letters can be anything and repeated

a) Total number of 3 letter stations possible is

b) Total number of 4 letter station possible is

c) Total station identification possible is

d) Firstly we need to have total number of 3 letter stations where all the letters are unique and that is equal to

So probability of all the 3 letters are different is

Hence this is the probability of 3 different letters in the 3 letter station code.

Thank you !!

orchestra answered 1 year ago

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