How many three-digit even numbers can be formed using the digits 1, 2, 3, 4 and 5 when repetition of digits is not allowed?a)36b)30c)24d)12Correct answer is option 'C'. Can you explain this answer?

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Answer

Answer

To find the number of three-digit even numbers that can be formed using the digits 1, 2, 3, 4, and 5 without repetition, we need to consider the following steps:

Step 1: Determine the possible choices for the hundreds digit.
Since the number must be even, the hundreds digit must be either 2 or 4. Thus, there are 2 choices for the hundreds digit.

Step 2: Determine the possible choices for the tens digit.
After choosing the hundreds digit, we are left with 4 remaining digits: 1, 3, 4, and 5. Since repetition is not allowed, the tens digit cannot be the same as the hundreds digit. Therefore, there are 3 choices for the tens digit.

Step 3: Determine the possible choices for the units digit.
After choosing the hundreds and tens digits, we are left with 3 remaining digits: 1, 3, and 5. Again, repetition is not allowed, so the units digit cannot be the same as the hundreds or tens digit. Therefore, there are 2 choices for the units digit.

Step 4: Multiply the choices from each step to find the total number of three-digit even numbers.
The total number of three-digit even numbers can be found by multiplying the number of choices for each step: 2 choices for the hundreds digit, 3 choices for the tens digit, and 2 choices for the units digit.

Total number of three-digit even numbers = 2 × 3 × 2 = 12

Therefore, the correct answer is option (d) 12.

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