a panel of contest judges is to consist of 13 women and 6 men. a list of potential judges includes 14 women and 8 men. how many different panels could be created from this list
To calculate the number of different panels that could be created, we need to determine the combinations of women and men that can be selected for the panel.
The number of different panels can be calculated using the combination formula:
C(n, r) = n! / (r! * (n - r)!)
Where:
n is the total number of potential judges
r is the number of judges to be selected
In this case, there are 14 women and 8 men to choose from, and we want to create a panel with 13 women and 6 men:
C(14, 13) * C(8, 6) = (14! / (13! * (14 - 13)!)) * (8! / (6! * (8 - 6)!))
Simplifying the equation:
C(14, 13) * C(8, 6) = 14 * 8
C(14, 13) = 14 as there is only one way to select 13 women from a group of 14
C(8, 6) = 8 * 7 / 2 = 28
C(14, 13) * C(8, 6) = 14 * 28 = 392
Therefore, the number of different panels that could be created from the list of potential judges is 392.
To determine the number of different panels that could be created, we can use combinations.
The number of ways to select a panel of 13 women from a list of 14 women can be calculated using the combination formula:
C(n, r) = n! / (r! * (n - r)!)
where n is the total number of items to choose from, and r is the number of items to select.
Using this formula:
C(14, 13) = 14! / (13! * (14 - 13)!)
Simplifying the equation:
C(14, 13) = 14
This means there are 14 different ways to select a panel of 13 women from the list of 14 women.
Similarly, the number of ways to select a panel of 6 men from a list of 8 men can be calculated using the combination formula:
C(8, 6) = 8! / (6! * (8 - 6)!)
Simplifying the equation:
C(8, 6) = 28
This means there are 28 different ways to select a panel of 6 men from the list of 8 men.
To find the total number of panels that can be created with a combination of women and men, we multiply the number of ways to select women with the number of ways to select men:
Total number of panels = 14 * 28 = 392
Therefore, there can be 392 different panels created from this list.