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 Z. 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?

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.CR: Chapter Review
Problem 70E: How many distinguishable words can be formed from the letters of the word casserole if each letter...
icon
Related questions
Question
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 Z. 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.)
Transcribed Image Text: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 Z. 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.)
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps

Blurred answer