Question
The number of numbers greater than 5000, less than 9000 and divisible by 3, that can be formed using the digits 0,1,2,5,9, if the repetition of the digits is allowed, is \_\_\_\_
JEE Main
Mathematics
Permutation Combination
2026
JEE Main 2026 (24 January Shift 1)
JEE Main Mathematics Question (2026) — Solution
Options
- A. A
- B. B
- C. C
- D. D
Answer
A. A
Step-by-step solution
(1) all different 5, 0, 1, 9 3 = 6 ways (2) 2 alike, 2 different 5, 0, 0, 1 3 ways 5, 1, 1, 2 3 ways 5, 2, 2, 0 3 ways 5, 2, 2, 9 3 ways 5, 5, 0, 2 6 ways 5, 5, 2, 9 6 ways 5, 1, 9, 9 3 ways (3) 3 alike, 1 different 5, 5, 5, 0 3 ways 5, 5, 5, 9 3 ways (4) 2 alike, 2 other alike 5, 5, 1, 1 3 ways Total ways = 42
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