Question

From the digits 0, 1, 2, 3, three-digit numbers are formed. Among that, the number of even numbers are:

• A. 6
• B. 10
• C. 12
• D. 18

Hint:

In such problems, ensure to count the possible choices for each place value and then calculate.

Answer 1

The Correct Option is B

To form a three-digit even number using the digits 0, 1, 2, 3, we must ensure that the last digit is an even number. Here, the even digits available are 0 and 2. Let's explore each case:

• Case 1: Last digit is 0
• Case 2: Last digit is 2

For Case 1 (last digit is 0), we select 2 remaining digits from {1, 2, 3} for the first two positions:

• Digits: _ _ 0
• First digit can be chosen from {1, 2, 3}, i.e., 3 choices.
• Second digit can be chosen from the remaining 2 digits
• Total for Case 1 = 3 x 2 = 6.

For Case 2 (last digit is 2), we select 2 remaining digits from {0, 1, 3} for the first two positions:

• Digits: _ _ 2
• First digit can be chosen from {1, 3}, since a number cannot start with 0, i.e., 2 choices.
• Second digit can be chosen from the remaining 2 digits.
• Total for Case 2 = 2 x 2 = 4.

Adding both cases gives the total number of even numbers: 6 (Case 1) + 4 (Case 2) = 10.

Last Digit	Possibilities
0	6
2	4
Total	10

Therefore, the number of even numbers that can be formed is 10.