-
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
Student Visas
-
Arts, Commerce & Sciences
Exams
Colleges
Upcoming Events
Resources
-
Management and Business Administration
Colleges & Courses
Predictors
-
Learn
Online Courses
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
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 8-letter passwords can be created using upper-case letters, lower-case letters, and digits (0-9) without repetition, if the password must contain at least one upper-case letter,
How many different 8-letter passwords can be created using upper-case letters, lower-case letters, and digits (0-9) without repetition, if the password must contain at least one upper-case letter, one lower-case letter, and any two digits 4 and 9?
5,496,740
1,466,640
7,345,980
4,546,345
Answers (1)
To solve this question, we can break it down into different cases:
Case 1: Selecting one upper-case letter, one lower-case letter, and two digits (4 and 9)
We can select one upper-case letter from the 26 available in C(26, 1) = 26 ways.
We can select one lower-case letter from the 26 available in C(26, 1) = 26 ways.
We can select one digit 4 from the 10 available in C(10, 1) = 10 ways.
We can select one digit 9 from the remaining 9 available in C(9, 1) = 9 ways.
Total options for Case 1 = 2626
10
9 = 60,840
Case 2: Selecting two upper-case letters, one lower-case letter, and two digits (4 and 9)
We can select two upper-case letters from the 26 available in C(26, 2) = 325 ways.
We can select one lower-case letter from the 26 available in C(26, 1) = 26 ways.
We can select one digit 4 from the 10 available in C(10, 1) = 10 ways.
We can select one digit 9 from the remaining 9 available in C(9, 1) = 9 ways.
Total options for Case 2 = 325 26
10
9 = 702,900
Case 3: Selecting one upper-case letter, two lower-case letters, and two digits (4 and 9)
We can select one upper-case letter from the 26 available in C(26, 1) = 26 ways.
We can select two lower-case letters from the 26 available in C(26, 2) = 325 ways.
We can select one digit 4 from the 10 available in C(10, 1) = 10 ways.
We can select one digit 9 from the remaining 9 available in C(9, 1) = 9 ways.
Total options for Case 3 = 26 325
10
9 = 702,900
Total number of different 8-letter passwords = Total options for Case 1 + Total options for Case 2 + Total options for Case 3 = 60,840 + 702,900 + 702,900 = 1,466,640
Therefore, the total number of different 8-letter passwords that can be created using upper-case letters, lower-case letters, and digits (0-9) without repetition, if the password must contain at least one upper-case letter, one lower-case letter, and any two digits 4 and 9, is 1,466,640.
JEE Main high-scoring chapters and topics
Study 40% syllabus and score up to 100% marks in JEE
