Q1:jipmat 2025QA › Permutation & CombinationEasyQA · MCQ

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?

• A36
• B30
• C24
• D12

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The Setup: We need to build a 3-digit number from the set $\{1, 2, 3, 4, 5\}$ without any repeating digits. To be an even number, the last digit has to pass the vibe check (it must be divisible by 2). Step 1: Fix the units digit. The only even digits in our squad are $2$ and $4$. That gives us $2$ valid options for the final slot. Step 2: Fill the remaining slots. We have a 3-digit number (Hundreds, Tens, Units). We used $1$ digit for the units place, leaving $4$ digits available. For the Hundreds place, we have $4$ options. For the Tens place, we have $3$ options. Step 3: Multiply them together using the Fundamental Principle of Counting. $$Total=4 \times 3 \times 2=24$$ Final Answer: 24