how many ways can a jury of six men and six women be selected from twelve men and ten women?
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To determine the number of ways a jury of six men and six women can be selected from twelve men and ten women, we can use the concept of combinations.
First, we need to calculate the number of ways to select six men from twelve. This can be done using the combination formula:
C(n, k) = n! / (k!(n-k)!)
In our case, n = 12 (number of men) and k = 6 (number of men to be selected). Plugging these values into the formula:
C(12, 6) = 12! / (6!(12-6)!)
= 12! / (6! x 6!)
Next, we need to calculate the number of ways to select six women from ten. Using the same combination formula:
C(n, k) = n! / (k!(n-k)!)
In this case, n = 10 (number of women) and k = 6 (number of women to be selected). Plugging these values into the formula:
C(10, 6) = 10! / (6!(10-6)!)
= 10! / (6! x 4!)
Finally, to find the total number of ways to select six men and six women for the jury, we multiply the number of ways to select six men with the number of ways to select six women:
Total number of ways = C(12, 6) x C(10, 6)
Now you can calculate the value by substituting the values into the formulas and evaluating the expressions.