Answer:
Step-by-step explanation:
In order for a number to be divisible by 4, its last two digits must be divisible by 4. This will be the case if either of these conditions holds:
We must count the ways these conditions can be met with the given digits.
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Since we only have even numbers to work with, the ones digit must be an even multiple of 2: 4 or 8. (The tens digit cannot be odd.) The digits 4 and 8 comprise half of the available digits, so half of all possible numbers made from these digits will be divisible by 4.
If the numbers must use each digit exactly once, there will be 4! = 24 of them. 24/2 = 12 of these 4-digit numbers will be divisible by 4.
Each of the four digits can have any of four values, so there will be 4^4 = 256 possible 4-digit numbers. Of these, 256/2 = 128 will be divisible by 4.
