Question
How many 4-digit numbers that are divisible by 4 can be formed using the digits 1, 2, 3 and 4 (repetition of digits is not allowed)?
NDA
Mathematics
Permutation Combination
2025
NDA 2025 (Phase 2)
NDA Mathematics Question (2025) — Solution
Options
- A. 3
- B. 6
- C. 9
- D. 12
Answer
B. 6
Step-by-step solution
A number is divisible by 4 if the number formed by its last two digits is divisible by 4. Using the digits 1, 2, 3, 4 without repetition, the possible two-digit numbers at the end that are divisible by 4 are 12, 24, and 32. For each of these endings, the remaining two digits can be arranged in the first two places in 2! = 2 ways. Total number of such 4-digit numbers is 3 2 = 6. Answer: 6
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