The digits 2, 3, 4, 7, and 8 are each used once in a random order to form a five-digit number. What is the probability that the resulting number is divisible by 4? Express your answer as a common fraction.
4/5
3/10
To find the probability that the resulting number is divisible by 4, we need to determine how many of the possible arrangements of the given digits will yield a number divisible by 4.
To be divisible by 4, a number must end in a two-digit number that is divisible by 4. In this case, the only two-digit numbers among the given digits that are divisible by 4 are 24 and 48.
Now we need to consider the possible arrangements of the other three digits. Since we have three digits remaining (3, 7, and 8), there are 3! = 6 different arrangements for these digits.
In conclusion, there are 2 possible two-digit endings that are divisible by 4 (24 or 48), and for each of these endings, there are 6 different arrangements for the remaining three digits.
Therefore, the total number of arrangements that result in a number divisible by 4 is 2 × 6 = 12.
Since there are 5 digits in total, there are 5! = 5 × 4 × 3 × 2 × 1 = 120 possible arrangements of the digits.
Thus, the probability that the resulting number is divisible by 4 is 12/120, which simplifies to 1/10.
Therefore, the answer is 1/10.