In a company's employee list, there are 10 male employees and 8 female employees. The company plans to select a group of these employees, including 3 male employees and 2 female employees, to attend an important business meeting. How many different selection methods are there?
Question
In a company's employee list, there are 10 male employees and 8 female employees. The company plans to select a group of these employees, including 3 male employees and 2 female employees, to attend an important business meeting. How many different selection methods are there?
Solution
This is a combination problem because the order in which the employees are selected does not matter.
The formula for combinations is:
C(n, k) = n! / [k!(n-k)!]
where:
- n is the total number of items
- k is the number of items to choose
- ! denotes factorial, which is the product of all positive integers up to that number
First, calculate the number of ways to choose 3 male employees from 10:
C(10, 3) = 10! / [3!(10-3)!] = 120
Next, calculate the number of ways to choose 2 female employees from 8:
C(8, 2) = 8! / [2!(8-2)!] = 28
Finally, multiply these two numbers together to find the total number of ways to select the group of employees:
120 * 28 = 3360
So, there are 3360 different ways to select the group of employees.
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