Question
Passage: A 4-digit number is selected at random formed by using the digits 0, 1, 2, 3 and 4 (where repetition of digits is not allowed). Question: What is the probability that the number selected is divisible by 2 ?
NDA
Mathematics
Permutation Combination
2026
NDA 2026 (Phase 1)
NDA Mathematics Question (2026) — Solution
Options
- A. 5 8
- B. 3 8
- C. 1 8
- D. 5 24
Answer
A. 5 8
Step-by-step solution
Total number of 4-digit numbers formed using 0, 1, 2, 3, 4 without repetition: The thousands place can be filled in 4 ways (excluding 0). The remaining 3 places can be filled in ^ 4 P_ 3 = 24 ways. Total numbers = 4 24 = 96. For the number to be divisible by 2, the units digit must be 0, 2, or 4. Case 1: Units digit is 0. The remaining 3 places can be filled in ^ 4 P_ 3 = 24 ways. Case 2: Units digit is 2 or 4. The units place can be filled in 2 ways. The thousands place can be filled in 3 ways (excluding 0 and the units digit). The remaining 2 places can be filled in ^ 3 P_ 2 = 6 ways. Number of such numbers = 2 3 6 = 36. Total number of even 4-digit numbers = 24 + 36 = 60. Required probability = 60 96 = 5 8 . Answer: 5 8
Related: Mathematics — Permutation Combination · All PYQ Banks