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The probability of forming a three digit numbers with all 3 digits being same when three digit numbers are formed out of the digit 0, 2, 4, 6, 8 is
A. \[\dfrac{1}{{16}}\]
B. \[\dfrac{1}{{12}}\]
C. \[\dfrac{1}{{645}}\]
D. \[\dfrac{1}{{25}}\]

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Last updated date: 17th Apr 2024
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Answer
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Hint: Here, we will find the probability of the event to happen by dividing the number of favorable outcomes by the total number of outcomes.

Complete step-by-step solution:
The given digits are 0, 2, 4, 6, 8.
We have to write these digits in hundreds, tens and ones places to form three digit numbers.

Since 0 cannot occupy the hundreds place, there are only 4 ways to fill the hundreds place.

Now, there are 5 ways to fill the tens place and 5 ways to fill the ones place.

We will find the total number of 3 digit numbers is formed using the given digits.

\[4 \times 5 \times 5 = 100\]

We know that the three digit numbers formed using given digits that have the same digits are 222, 444, 666 and 888.

We will now find the probability of forming a three digit number having the same digits.

\[
  \dfrac{{{\text{Number of 3 digit numbers having same digits}}}}{{{\text{Total number of 3 digit numbers using the given digits}}}} = \dfrac{4}{{100}} \\
   = \dfrac{1}{{25}} \\
\]

Thus, the probability of forming a three digit number with all 3 digits being the same is \[\dfrac{1}{{25}}\].

Hence, the option D is correct.

Note: In this question, some students include 0 in the hundreds place which is wrong. Students should know the concept of probability before solving this question. Also, we are supposed to write the values properly to avoid any miscalculation.