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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?

 

Option: 1

12


Option: 2

16


Option: 3

14


Option: 4

10


Answers (1)

best_answer

To calculate the number of ways a team of 3 males and 2 females can be formed from a company with 5 male and 5 female employees, where no two males are from the same department, we can proceed as follows:

First, we select 3 males from the 5 available. Since no two males can be from the same department, we cannot choose more than 1 male from any single department. Therefore, we need to consider the possibilities for each department.

Let's assume the company has 3 departments: Department A, Department B, and Department C.

Case 1: Selecting 3 males from different departments

For this case, we choose 1 male from each department. The number of ways to choose 1 male from Department A, 1 male from Department B, and 1 male from Department C is:

(Number of males in Department A) \times (Number of males in Department B) \times(Number of males in Department C) = 2 \times2\times 2 = 8.


Case 2: Selecting 2 males from one department and 1 male from a different department

For this case, we choose 2 males from one department and 1 male from another department. There are 3 ways to choose the department with 2 males and 2 ways to choose the department with 1 male. The number of ways to select the males within each department is:

(Number of ways to choose department with 2 males)\times (Number of ways to choose department with 1 male)\times (Number of ways to choose 2 males from the selected department) (Number of ways to choose 1 male from the other selected department) =.3\times 2\times \left ( C\left ( 2,2 \right ) \right )\times \left ( C\left ( 2,1 \right ) \right )= 6.

Therefore, the total number of ways to form a team of 3 males and 2 females, where no two males are from the same department, is:

Total = Case 1 + Case 2 = 8 + 6 = 14.

Hence, there are 14 distinct ways to form a team of 3 males and 2 females, where no two males are from the same department, from a company with 5 male and 5 female employees.

 

Posted by

manish painkra

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