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

• \[\frac{1}{16}\]

   

• \[\frac{16}{25}\]

   

• \[\frac{1}{645}\]

   

• \[\frac{1}{25}\]

   

Answer 1

The given digits are 0, 2, 4, 6, 8.

____	____	____
Hundreds	Tens	Ones

Now, there are 4 ways to fill the hundreds place (0 cannot occupy the hundreds place), 5 ways to fill the tens place and 5 ways to fill the ones place.
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) = \[\frac{\text{ Number of 3 digit numbers that have the same digits} }{\text{ Total number of 3 digit numbers formed using the given digits} } = \frac{4}{100} = \frac{1}{25}\]