Question

A contractor is required by a county planning department to submit one, two, three, four, or five forms (depending on the nature of the project) in applying for a building permit. Let Y= the number of forms required submit to get the building permit. The probability that y forms are required is known to be proportional to √y​. That is, f(y)=P(Y=y)=k√y for y=1,…,5. Suppose there are 5 contractors applying for a building permit. What is the probability that they will all have a different amount of forms to fill out?

Answer 1

To find the probability that all five contractors will have a different amount of forms to fill out, we consider the different possible combinations of forms. The probability is 1/120.

Step-by-step explanation:

To find the probability that all five contractors will have a different amount of forms to fill out, we need to consider the different possible combinations of forms for each contractor.

Since there are 5 contractors and each contractor can fill out either 1, 2, 3, 4, or 5 forms, the total number of possible combinations is 5!

Out of these combinations, we want to find the ones where each contractor has a different number of forms to fill out, which means there are no duplicates. There are 5 options for the first contractor, 4 options for the second contractor, 3 for the third, 2 for the fourth, and 1 for the fifth.

Therefore, the probability that all contractors will have a different amount of forms to fill out is (5 * 4 * 3 * 2 * 1) / (5!) = 1/120.