Q.64 Given digits 2, 2, 3, 3, 3, 4, 4, 4, 4,
how many distinct 4-digit numbers greater than 3000 can be formed?
Options:
(A) 50
(B) 51
(C) 52
(D) 54
How Many Distinct 4-Digit Numbers Greater Than 3000 Can Be Formed?
Questions based on permutations and combinations of digits are common in competitive
exams such as SSC, Banking, Railway, and CAT. This problem focuses on forming distinct
four-digit numbers under given restrictions.
Given Data
Digits provided:
2, 2, 3, 3, 3, 4, 4, 4
- The number must be a 4-digit number
- The number must be greater than 3000
- Digits cannot be used more than their given frequency
- All numbers formed must be distinct
Key Observation
For a number to be greater than 3000, the thousands digit must be either
3 or 4. Hence, we consider two separate cases.
Case 1: Thousands Digit = 3
After using one digit 3, the remaining digits are:
2, 2, 3, 3, 4, 4, 4
We now arrange any 3 digits from these remaining digits in the hundreds, tens,
and units places, accounting for repetition.
Total distinct numbers formed in this case = 24
Case 2: Thousands Digit = 4
After using one digit 4, the remaining digits are:
2, 2, 3, 3, 3, 4, 4
Arranging any 3 digits from these remaining digits gives:
Total distinct numbers formed in this case = 28
Total Count
Total numbers greater than 3000 =
24 + 28 = 52
Correct Answer
Option (C): 52
Conclusion
By considering place value restrictions and repetition of digits, the total number
of distinct four-digit numbers greater than 3000 that can be formed is:
52
