How many four-digit even number can be formed using the digits 0, 1, 2, 3 and 4. If repetition of the digits is not permitted?

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answer is C.

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Detailed Solution

Let the total no. of digits be 5.
Case 1: Numbers that have unit digit 0.
When the unit digit is 0, there may be

5 − 1 = 4

digits available to fill the remaining three spaces. If repetition is not permitted, the thousandth place can be held by any four digits from (1,2,3,4), after which we have

4 − 1 = 3

digits remaining, so the hundredth place can be filled with any of the three digits, and the tenth place can be filled with any of the two digits.
The total number of ways is

4 × 3 × 2 = 24

.
Case 2: Numbers that end with 2 or 4.
If the number's unit digit is 2, we have

5 − 1 = 4

digits left (0,1,3,4). The thousandth digit of the number can be filled in one of three ways (1,3,4), but it cannot be zero or it will generate a three-digit number. The hundredth digit of the number can be filled in three different ways (including 0 and any other digit left). Similarly, the tenth digit of the number can be filled in two different ways (including 0 and any other digit left)
The total number of ways is