Question

Every radio and television station in the United States has a unique call name. Each contains three or four letters, beginning with $\mathrm{K}$ or $\mathrm{W}$ . For example, KEY and WASP are legal call names. Find the number of possible call names.

Name: Problem 33, Chapter 6: Discrete Mathematics with Applications
Uploaded: 2020-08-20T21:24:08-08:00
Duration: 3 min 58 s
Channel: Ankit Gupta
Description: Every radio and television station in the United States has a unique call name. Each contains three or four letters, beginning with K or W . For example, KEY and WASP are legal call names. Find the number of possible call names.

   Every radio and television station in the United States has a unique call name. Each contains three or four letters, beginning with $\mathrm{K}$ or $\mathrm{W}$ . For example, KEY and WASP are legal call names. Find the number of possible call names.

Discrete Mathematics with Applications

Thomas Koshy 1st Edition

Chapter 6, Problem 33

Instant Answer

Solved by Expert Ankit Gupta

08/20/2020

Step 1

Since it can be either $\mathrm{K}$ or $\mathrm{W}$, there are 2 options. Show more…

Show all steps

Thanks for your feedback!

Every radio and television station in the United States has a unique call name. Each contains three or four letters, beginning with $\mathrm{K}$ or $\mathrm{W}$ . For example, KEY and WASP are legal call names. Find the number of possible call names.

Play audio

Feedback

Ankit Gupta and 82 other subject Algebra educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Fundamental Counting Principle

This principle states that if an event can occur in several independent stages with a certain number of choices at each stage, the total number of outcomes is the product of the number of choices at each stage. It is essential for breaking down multi-step counting problems.

Case Analysis

Case analysis involves splitting a problem into mutually exclusive scenarios based on distinct conditions, solving each case separately, and then combining the results to obtain the total count. This systematic approach is particularly useful when different cases have different constraints.

Counting with Fixed-Length Strings

This concept involves determining the number of possible sequences of a fixed length where choices for each position are made from a given set of symbols, often with additional restrictions on certain positions. It is a common application of both the fundamental counting principle and case analysis in combinatorics.

Please give Ace some feedback