A 6-digit phone number cannot start with 0 or 1. Assume that there are no restrictions on the remaining 5 numbers. How many telephone numbers are possible in which all 6 digits are different? ..... The possible number of 6-digit telephone numbers where all the digits are different is
A 6-digit phone number cannot start with 0 or 1. Assume that there are no restrictions on the remaining 5 numbers. How many telephone numbers are possible in which all 6 digits are different? ..... The possible number of 6-digit telephone numbers where all the digits are different is
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![**Problem Statement:**
A 6-digit phone number cannot start with 0 or 1. Assume that there are no restrictions on the remaining 5 numbers. How many telephone numbers are possible in which all 6 digits are different?
**Solution Explanation:**
1. **First Digit Options:**
- The first digit can be any number from 2 to 9, giving us 8 possible choices.
2. **Remaining Digits:**
- After choosing the first digit, 9 digits remain (0 through 9 excluding the chosen first digit).
- The second digit can then be any of the 9 remaining digits.
- The third digit can be any of the remaining 8 digits.
- The fourth digit can be any of the 7 remaining digits.
- The fifth digit can be any of the 6 remaining digits.
- The sixth digit can be any of the 5 remaining digits.
3. **Total Combinations:**
- Multiply the choices for each digit position to find the total number of possible combinations:
\[
8 \times 9 \times 8 \times 7 \times 6 \times 5
\]
Therefore, the possible number of 6-digit telephone numbers where all the digits are different is the result of this calculation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc6d3e995-1d49-4d64-8a29-c93485532523%2F56945508-98e7-42a0-93a1-ced168a25b28%2F682mb4_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A 6-digit phone number cannot start with 0 or 1. Assume that there are no restrictions on the remaining 5 numbers. How many telephone numbers are possible in which all 6 digits are different?
**Solution Explanation:**
1. **First Digit Options:**
- The first digit can be any number from 2 to 9, giving us 8 possible choices.
2. **Remaining Digits:**
- After choosing the first digit, 9 digits remain (0 through 9 excluding the chosen first digit).
- The second digit can then be any of the 9 remaining digits.
- The third digit can be any of the remaining 8 digits.
- The fourth digit can be any of the 7 remaining digits.
- The fifth digit can be any of the 6 remaining digits.
- The sixth digit can be any of the 5 remaining digits.
3. **Total Combinations:**
- Multiply the choices for each digit position to find the total number of possible combinations:
\[
8 \times 9 \times 8 \times 7 \times 6 \times 5
\]
Therefore, the possible number of 6-digit telephone numbers where all the digits are different is the result of this calculation.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman