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.
use prob, last digit has to be either 2,4, or 8 to be divisible by 4, and the tens digit for 2 will be either 3 or 7. for 4, it has to be either 2 or 8, and for 8, it will be either 2 or 4. 3*2
=6, and arrange the rest of the digits appropriately...i think...
3/10
To find the probability that the resulting number is divisible by 4, we need to determine the total number of possible combinations and the number of combinations that are divisible by 4.
First, let's determine the total number of possible combinations. Since there are 5 digits and each digit can only be used once, there are 5 choices for the first digit, 4 choices for the second digit, 3 choices for the third digit, 2 choices for the fourth digit, and 1 choice for the fifth digit. Thus, there are 5! (5 factorial) or 120 total combinations.
Now, let's determine the number of combinations that are divisible by 4. A number is divisible by 4 if the last two digits form a number divisible by 4.
Out of the given digits (2, 3, 4, 7, and 8), the possible last digits that are divisible by 4 are 24, 28, 32, 48, 72, and 84. Therefore, there are 6 choices for the last two digits.
For the remaining three digits, we have 3 choices for the first remaining digit (since we cannot choose 2 or 4 as they are already used as a last digit), 2 choices for the second remaining digit, and 1 choice for the last remaining digit. So there are 3! or 6 possible combinations for the remaining three digits.
Multiplying the number of choices for the last two digits (6) by the number of choices for the remaining three digits (6), we get a total of 6 * 6 = 36 combinations that are divisible by 4.
Finally, the probability of getting a number divisible by 4 is given by the number of combinations that are divisible by 4 divided by the total number of possible combinations.
P(divisible by 4) = number of combinations divisible by 4 / total number of possible combinations = 36 / 120 = 3/10
Therefore, the probability that the resulting number is divisible by 4 is 3/10 or 0.3.