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How many ways can a jury of 6 men and 6 women be selected from 10 women and 12 men?
That would be the number of possible combinations of men, multiplied by the number of possible combinations of men. For each subset, the total number of possible combinations will be the factorial of the number available, divided by the factorial of that number minus six. In other words:
x = 10!/(10 - 6)! * 12!/(12-6)!
∴ x = 10!/4! * 12!/6!
∴ x = (10 * 9 * 8 * 7 * 6 * 5) * (12 * 11 * 10 * 9 * 8 * 7)
∴ x = 151200 * 665280
∴ x = 100590336000
So there are one hundred billion, five-hundred-and-ninety million, three-hundred-and-thirty-six thousand possible jury combinations from that selection.
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