A company has 12 male and 10 female employees, and needs to nominate 3 men and 3 women for the company bowling team. How many different teams can be formed?
number of ways of choosing male employees
N1=12C3=12!/(3!9!)
number of ways of choosing female employees
N2=10C3=10!/(3!9!)
Number of possible teams
=N1*N2
To determine the number of different teams that can be formed, we need to calculate the combination.
The number of ways to choose 3 men out of 12 can be calculated using the combination formula "nCr", which is:
12C3 = 12! / (3! * (12 - 3)!) = 12! / (3! * 9!) = (12 * 11 * 10) / (3 * 2 * 1) = 220.
Similarly, the number of ways to select 3 women out of 10 can be calculated as:
10C3 = 10! / (3! * (10 - 3)!) = 10! / (3! * 7!) = (10 * 9 * 8) / (3 * 2 * 1) = 120.
To find the number of different teams that can be formed, we multiply the number of ways to choose 3 men by the number of ways to choose 3 women:
220 * 120 = 26,400.
Therefore, there are 26,400 different teams that can be formed.
To find the number of different teams that can be formed with 3 men and 3 women, we can use the concept of combinations.
We need to select 3 men from a group of 12, so we can use the combination formula:
C(n, r) = n! / (r! * (n-r)!)
Here, n represents the total number of options (12 men) and r represents the number of selections (3 men).
So, for selecting 3 men out of 12, the calculation would be:
C(12, 3) = 12! / (3! * (12-3)!)
C(12, 3) = 12! / (3! * 9!)
Simplifying further:
C(12, 3) = (12 * 11 * 10) / (3 * 2 * 1)
C(12, 3) = 220
Therefore, there are 220 different teams that can be formed with 3 men from a group of 12.
Similarly, we can calculate the number of teams formed with 3 women from a group of 10 using the combination formula:
C(10, 3) = 10! / (3! * (10-3)!)
C(10, 3) = 10! / (3! * 7!)
Simplifying further:
C(10, 3) = (10 * 9 * 8) / (3 * 2 * 1)
C(10, 3) = 120
Therefore, there are 120 different teams that can be formed with 3 women from a group of 10.
Since these events are independent, we can multiply the number of teams for each gender to find the total number of different teams:
Total number of different teams = Number of teams with men * Number of teams with women
Total number of different teams = 220 * 120
Total number of different teams = 26,400
Hence, there can be 26,400 different teams formed, with 3 men and 3 women, from the given employee pool.