there are 8 students auditioning for a play and there are 56 possible outcomes. How many roles are there?

I am trying to help my son and I understand the question -just not sure how to get there as I am not understanding probabilities and combinations which I believe this is.

There are 8 ways to choose the first role, leaving 7 ways to choose the 2nd role, 6 ways for the 3rd, etc.

8*7 = 56, so we must have just two roles.

To find the number of roles in the play, we need to analyze the relationship between the number of students auditioning and the total number of possible outcomes.

Let's assume that each student can be assigned exactly one role, and there are no multiple roles for any student.

The total number of possible outcomes is given as 56. These outcomes represent all the different ways roles can be assigned to the students. Therefore, by understanding the relationship between the number of students and the number of outcomes, we can determine the number of roles available.

Let's start solving this problem step-by-step:

1. We know that there are 8 students auditioning for the play.
2. The total number of possible outcomes when assigning roles is 56.

Now, let's think about how to find the number of roles available:

To determine the number of roles, we can consider the scenario of assigning roles one by one to each student. For the first role, any of the 8 students can be selected. Once the first role is assigned, there are only 7 students left for the second role, then 6 for the third, and so on.

Therefore, to calculate the number of roles, we need to consider the product of the number of students available for each role.

Let's break down the calculation:

Number of roles = Number of students available for the first role × Number of students available for the second role × Number of students available for the third role × ... × Number of students available for the last role.

Using this approach, the calculation can be represented as:

Number of roles = 8 × 7 × 6 × ... × 1

Now, we can evaluate this expression to find the number of roles:

Number of roles = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

Computing this expression gives us:

Number of roles = 40,320

Therefore, there are 40,320 roles available in the play.