Suppose you are managing 25 employees, and you need to form three teams to work on three different projects.

Assume that all employees will work on exactly one team. Also, each employee has the same qualifications/skills, so any employee can serve on any team.

The number of employees on each project are as follows: 8 on Team A, 3 on Team B, and 14 on Team C

1)How many ways can Team A be selected from the available employees?

2)Then, how many ways can Team B be selected from the remaining available employees?

3)Then, how many ways can Team C be selected from the remaining available employees?

4)Then, how many ways can all teams be selected?

5)What is the probability that three workers randomly selected from all employees will all be from team A?

1. number of team A = C(25,8)

2. number of team B = C(17,3)
3. number of team C = C(14,14)
4. multiply them
5. C(22,5) x C(17,3) x C(14,14) / (answer to 4)

Sorry I'm kind of confused.. when you put C(25,8) I don't really know what that means or how to solve it.

To answer these questions, we can use the concept of combinations. In mathematics, combinations are used to calculate the number of ways to select items from a larger set without regard to the order in which they are selected. The formula for calculating combinations is given by:

nCr = n! / (r!(n - r)!)

Where n represents the total number of items and r represents the number of items to be chosen.

1) To find the number of ways Team A can be selected, we need to choose 8 employees from a total of 25. Therefore, the calculation is:

C(25, 8) = 25! / (8!(25 - 8)!)

2) After selecting Team A, we have 17 remaining employees to choose from for Team B. We need to choose 3 employees from this group. The calculation is:

C(17, 3) = 17! / (3!(17 - 3)!)

3) Similarly, after selecting Team A and Team B, we have 14 remaining employees for Team C. We need to choose 14 employees from this group. The calculation is:

C(14, 14) = 14! / (14!(14 - 14)!)

4) To calculate the number of ways all teams can be selected, we multiply the combinations from each team:

C(25, 8) * C(17, 3) * C(14, 14)

5) Finally, to calculate the probability of randomly selecting 3 workers, all from Team A, we calculate the probability of selecting 3 workers from Team A and divide it by the total number of ways 3 workers can be chosen from all employees:

C(8, 3) / C(25, 3) = (8! / (3!(8 - 3)!)) / (25! / (3!(25 - 3)!))