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- A company has 5 male and 5 female employees. In how many ways can a team of 3 males and 2 females be formed, where no two males are from the same department? <div class='qna-opt
A company has 5 male and 5 female employees. In how many ways can a team of 3 males and 2 females be formed, where no two males are from the same department?
12
20
18
24
Answers (1)
To calculate the number of ways a team of 4 males and 2 females can be formed from a company with 8 male and 6 female employees, where no two males are from the same department, we can use the following approach:
Assuming the company has three departments, we can consider the cases where the males are selected from different departments.
Case 1: Selecting 4 males from different departments
For this case, we choose 1 male from each department. The number of ways to choose 1 male from each department is:
(Number of males in Department 1) (Number of males in Department 2)
(Number of males in Department 3) = 2
2
2 = 8.
Case 2: Selecting 3 males from one department and 1 male from a different department
For this case, we choose 3 males from one department and 1 male from another department. There are three possible departments to choose from for the 3 males and two possible departments for the remaining male. The number of ways to select the males within each department is:
(Number of ways to choose department with 3 males) (Number of ways to choose department with 1 male)
(Number of ways to choose 3 males from the selected department) (Number of ways to choose 1 male from the other selected department) = 3
2
(C(3, 3))
(C(2, 1)) = 3
2
1
2 = 12.
Therefore, the total number of ways to form a team of 4 males and 2 females, where no two males are from the same department, is:
Total = Case 1 + Case 2 = 8 + 12 = 20.
Hence, there are 20 distinct ways to form a team of 4 males and 2 females, where no two males are from the same department, from a company with 8 male and 6 female employees.
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