-
Engineering and Architecture
Exams
Colleges
Predictors
Resources
-
Computer Application and IT
Quick Links
Colleges
-
Pharmacy
Colleges
Resources
-
Hospitality and Tourism
Colleges
Resources
Diploma Colleges
-
Competition
Other Exams
Resources
-
School
Exams
Top Schools
Products & Resources
-
Study Abroad
Top Countries
Resources
-
Arts, Commerce & Sciences
Colleges
Upcoming Events
Resources
-
Management and Business Administration
Exams
Colleges & Courses
Predictors
-
Learn
Law Preparation
MBA Preparation
Engineering Preparation
Medical Preparation
-
Online Courses and Certifications
Top Streams
Specializations
- Digital Marketing Certification Courses
- Cyber Security Certification Courses
- Artificial Intelligence Certification Courses
- Business Analytics Certification Courses
- Data Science Certification Courses
- Cloud Computing Certification Courses
- Machine Learning Certification Courses
- View All Certification Courses
Resources
-
Medicine and Allied Sciences
Colleges
Predictors
Resources
-
Law
Resources
Colleges
-
Animation and Design
Exams
Predictors & Articles
Colleges
Resources
-
Media, Mass Communication and Journalism
Colleges
Resources
-
Finance & Accounts
Top Courses & Careers
Colleges
Get Answers to all your Questions
- Home
- Engineering
- How many different four-digit numbers can be formed using the digits 1, 4, 5, 6, 7, 8, and 9 if repetition is allowed and ten's position is filled with the perfect square of 3?
How many different four-digit numbers can be formed using the digits 1, 4, 5, 6, 7, 8, and 9 if repetition is allowed and ten's position is filled with the perfect square of 3?
542
625
343
595
Answers (1)
To calculate the number of different four-digit numbers that can be formed using the digits 1, 4, 5, 6, 7, 8, and 9, with repetition allowed and the ten's position filled with the perfect square of 3, we can proceed as follows:
The perfect square of 3 is 9, so for the ten's position, we have only one option, which is 9.
For the thousands position, any of the seven available digits can be chosen (1, 4, 5, 6, 7, 8, or 9) since repetition is allowed.
For the hundreds position, any of the seven available digits can be chosen.
For the one's position, any of the seven available digits can be chosen as well.
Therefore, the number of different four-digit numbers that can be formed is obtained by multiplying the choices for each position:
Number of choices for the ten's position = 1 (since it is fixed as 9)
Number of choices for the thousands position = 7 (since any of the seven digits can be chosen)
Number of choices for the hundreds position = 7 (any of the seven digits can be chosen)
Number of choices for the one's position = 7 (any of the seven digits can be chosen)
Total number of different four-digit numbers = Number of choices for the ten's position Number of choices for the thousands position
Number of choices for the hundreds position
Number of choices for the one's position
= 1 7
7
7
= 343
Therefore, there are 343 different four-digit numbers that can be formed using the digits 1, 4, 5, 6, 7, 8, and 9, with repetition allowed and the ten's position filled with the perfect square of 3 (9).
JEE Main high-scoring chapters and topics
Study 40% syllabus and score up to 100% marks in JEE
