Playing mixed doubles
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This is a great way of doing it if we canshankyrams wrote:I think the answer is 105.
If there are X*Y people who are put in X groups containing Y people each the this can be done in [ (X*Y) ! / ((X!)*(Y^X)) ] ways.
(1) identify the problem and remember the formula in the heat of the test
(2) be careful in not confusing some other problem as this problem and end up with the wrong answer.