A company has 11 male and 10 female employees, and needs to nominate 2 men and 2 women for the company bowling team. How many different teams can be formed?
To find the number of different teams that can be formed, we will use the combination formula.
The number of ways to choose 2 men out of 11 is given by:
C(11, 2) = 11! / (2! * (11-2)!) = 11! / (2! * 9!) = (11 * 10) / (2 * 1) = 55
So, there are 55 different ways to choose 2 men from 11.
Similarly, the number of ways to choose 2 women out of 10 is given by:
C(10, 2) = 10! / (2! * (10-2)!) = 10! / (2! * 8!) = (10 * 9) / (2 * 1) = 45
So, there are 45 different ways to choose 2 women from 10.
To find the total number of different teams, we multiply the number of ways to choose 2 men by the number of ways to choose 2 women:
Total number of different teams = 55 * 45 = 2475
Therefore, there are 2475 different teams that can be formed.
To find out the number of different teams that can be formed, we need to use combinations.
First, let's calculate the number of ways we can choose 2 men from the 11 male employees. This is denoted as "11 choose 2" or simply C(11, 2).
The formula for combinations is: C(n, r) = n! / (r! * (n - r)!)
where n is the total number of items to choose from, r is the number of items we want to choose, and "!" denotes factorial.
For the male employees:
C(11, 2) = 11! / (2! * (11 - 2)!)
= 11! / (2! * 9!)
= (11 * 10 * 9!) / (2! * 9!)
= (11 * 10) / 2
= 55
Now, let's calculate the number of ways we can choose 2 women from the 10 female employees. This is denoted as "10 choose 2" or C(10, 2).
For the female employees:
C(10, 2) = 10! / (2! * (10 - 2)!)
= 10! / (2! * 8!)
= (10 * 9 * 8!) / (2! * 8!)
= (10 * 9) / 2
= 45
Finally, to find the total number of different teams that can be formed, we need to multiply these two combinations:
Total number of teams = C(11, 2) * C(10, 2)
= 55 * 45
= 2475
Therefore, there can be 2475 different teams formed from the given employees.