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Question
Three digit numbers are formed with the digits 0, 2, 4, 6 and 8. Write the probability of forming a three digit number with the same digits.
Solution
\[\text{ Total 3-digit numbers that can be made out of0, 2, 4, 6 and 8 = 4 } \times 5 \times 5 \left( \text{ hundreds place cannot be filled with 0 } \right)\]
\[ = 100\]
\[\text{ But 222, 444, 666 and 888are four numbers, which have the same digits at all places } .\]
\[P\left(\text{ 3-digit number having same digits at all places} \right) = \frac{4}{100}\]
\[ = \frac{1}{25}\]
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