Discussion
How many 3-digit numbers can be formed using three distinct single digit prime numbers?
Answer: B
The answer is 24.
The single-digit primes are 2, 3, 5 and 7, four in all. A 3-digit number using three distinct ones is an ordered arrangement of 3 of these 4 digits, and none of them is 0, so every arrangement is a valid 3-digit number:
\[ ^{4}P_{3} = 4 \times 3 \times 2 = 24 \]
64 is \(4^{3}\), which allows digits to repeat (22, 233 and so on), against the word 'distinct'. 4 counts only the choice of which three primes to use, \(^{4}C_{3}\), and forgets that each choice can be ordered in 6 ways. 12 counts only two of the three places.
No comment is present. Be the first to comment.
Loading…
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development