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.
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
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