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.

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Solution

$Total 3-digit numbers that can be made out of 0, 2, 4, 6 and 8 = 4 \times 5 \times 5 (hundreds place cannot be filled with 0) = 100 But 222, 444, 666 and 888 are four numbers, which have the same digits at all places. P (3-digit number having same digits at all places) = \frac{4}{100} = \frac{1}{25}$

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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.

Total 3-digit numbers that can be made out of 0, 2, 4, 6 and 8=4×5×5 hundreds place cannot be filled with 0=100But 222, 444, 666 and 888 are four numbers, which have the same digits at all places.P3-digit number having same digits at all places=4100=125