Concept explainers
To calculate: The number of 3-letter code if at least one of the letters is vowels.
Answer to Problem 20WE
The number of 3-letter code if at least one of the letters is vowelsare
Explanation of Solution
Given information:
3-letter code is to be formed and at least one of letter should be vowel.
Formula used:
Fundamental counting principle states that if there are m ways to make a selection and n ways to make a second selection then there are
Calculation:
Consider the provided information that 3-letter code is to be formed and at least one of letter should be vowel.
There are 5 vowels and 21 consonants.
Let 3-letter code wordbe
Case I: Only 1 vowel is there.
To select the first letter 5 choices are there among vowel.
The remaining two boxes can be consonants and each box has 21 possibilities
Recall that Fundamental counting principle states that if there are m ways to make a selection and n ways to make a second selection then there are
Therefore, the number of ways to select are,
Case II: Only 2 vowels are there.
To select the first letter 5 choices are there among vowel.
To select the second letter 5 choices are there among vowel.
The remaining box can be consonant and has 21 possibilities
Recall that Fundamental counting principle states that if there are m ways to make a selection and n ways to make a second selection then there are
Therefore, the number of ways to select are,
Case III: All 3 vowels are there.
To select the first letter 5 choices are there among vowel.
To select the second letter 5 choices are there among vowel.
To select the third letter 5 choices are there among vowel.
Recall that Fundamental counting principle states that if there are m ways to make a selection and n ways to make a second selection then there are
Therefore, the number of ways to select are,
Therefore, total number of 3-letter codes are,
Thus, the number of 3-letter code if at least one of the letters is vowels are
Chapter 15 Solutions
Algebra and Trigonometry: Structure and Method, Book 2
Additional Math Textbook Solutions
Linear Algebra and Its Applications (5th Edition)
College Algebra with Modeling & Visualization (6th Edition)
Intermediate Algebra (7th Edition)
Intermediate Algebra for College Students (7th Edition)
College Algebra (7th Edition)
A Graphical Approach to College Algebra (6th Edition)
- Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education