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Question
Three-digit numbers are formed using the digits 0, 2, 4, 6, 8. A number is chosen at random out of these numbers. What is the probability that this number has the same digits?
Options
`1/16`
`16/25`
`1/645`
`1/25`
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Solution
`1/25`
Explanation:
Since a 3-digit number cannot start with digit 0.
The hundredth place can have any of the 4 digits.
Now, the tens and units place can have all the 5 digits.
Therefore, the total possible 3-digit numbers are 4 × 5 × 5
i.e., 100.
The total possible 3 digit numbers having all digits same = 4
Hence, P(3-digit number with same digits) = `4/100 = 1/25`.
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