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Question
Without repetition of the numbers, four-digit numbers are formed with the numbers 0, 2, 3, 5. The probability of such a number divisible by 5 is ______.
Options
`1/5`
`4/5`
`1/30`
`5/9`
Solution
Without repetition of the numbers, four-digit numbers are formed with the numbers 0, 2, 3, 5. The probability of such a number divisible by 5 is `5/9`.
Explanation:
Four digit number using the digits 0, 2, 3, 5 without repetition and divisible by 5 with the given conditions is
If unit place be filled with 0
| 3 | 2 | 1 | 1 |
Then the number of ways = 3 × 2 × 1 × 1 = 6
If unit place be filled with 5
| 2 | 2 | 1 | 1 |
Then the number of ways = 2 × 2 × 1 × 1 = 4
∴ Total number of ways = 6 + 4 = 10
Total number of ways of arranging the digits 0, 2, 3, 5 to form 4-digit numbers without repetition is 3 × 3 × 2 × 1 = 18
∴ Required probability = `10/18 = 5/9`.
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