Question

Six male and six female dancers perform the virginia reel. This dance requiresthat they form a line consisting of six male/female pairs. How many such arrangementsare there

Answer 1

Solution -

We have 6 males and 6 females. And in each group we have to choose one male and a female

For the first group we have (6,6) options, after choosing one pair we have (5,5) options, then (4,4) options, then (3,3) options, then (2,2) options, then (1,1) options.

So the first has 36 possibilities, 6 possible males, 6 possible females. 6 times 6 is 36.  

After picking up one male and female, we have 5 males and 5 females, 25 possibilities and so on.

Total we have 36×25×16×4×1 = 57600.