Final answer:
To find the sum of all distinct five-digit positive integers formed using the given digits, calculate the average of the digits and multiply it by the total number of integers.
Step-by-step explanation:
Camy wants to find the sum of all distinct five-digit positive integers that can be formed using the digits 1, 3, 4, 5, and 9 exactly once in each integer. To find the sum, we need to calculate the average of these integers and then multiply it by the total number of integers.
The average of the digits is (1 + 3 + 4 + 5 + 9) / 5 = 22 / 5 = 4.4. Since each digit will appear in each position once, the sum of each position will be 4.4 times 10^4, 4.4 times 10^3, and so on.
Adding all the sums together, we get: 4.4 * (10^4 + 10^3 + 10^2 + 10^1 + 10^0) = 4.4 * (11111) = 48888.