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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
- \[\frac{1}{16}\]
- \[\frac{16}{25}\]
- \[\frac{1}{645}\]
- \[\frac{1}{25}\]
Solution
The given digits are 0, 2, 4, 6, 8.
| ____ | ____ | ____ |
| Hundreds | Tens | Ones |
Total number of 3 digit numbers formed using the given digits = 4 × 5 × 5 = 100
The three digit numbers formed using given digits that have the same digits are 222, 444, 666 and 888.
Number of 3 digit numbers that have the same digits = 4
∴ P(three digit number formed has the same digits) = \[\frac{\text{ Number of 3 digit numbers that have the same digits} }{\text{ Total number of 3 digit numbers formed using the given digits} } = \frac{4}{100} = \frac{1}{25}\]
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