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 ?

• A. $\frac{1}{16}$
• B. $\frac{16}{25}$
• C. $\frac{1}{645}$
• D. $\frac{1}{25}$

Answer 1

The correct option is D

$\frac{1}{25}$

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

$\overline{Hundreds}\overline{Tens}\overline{Ones}$

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 $=4\times 5\times 5=100$

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

$\therefore$ P(three digit number formed has the same digits)

$=\frac{\text{Number of 3 digit numbers that have the same digits}}{Totalnumberof3digitnumbersformedbyusingthegivendigits}=\frac{4}{100}=\frac{1}{25}$

Hence, the correct answer is option (d).