Problem: How many ways can a twelve member cheerleading squad(6 men and 6 women) pair up to form 6 male-female teams? What might the number 6!6!2^6 represent? What might the number 6!6!2^6*2^12 represent?
For first question there are 6! = 720 ways. For the second and third questions can someone please help me understand? Thank you very much for any feedback.
this is the number of bijections between two sets with $n$ elements each. This is $n!$
$(6!)(6!)2^6$ could be the number of ways to arrange the men and woman on a stage with $12$ positions (2 rows and 6 columns) so the men are in the back and the women in the front. And then selecting which columns are going to have the lights pointed at
$6!6!2^62^{12}$ could be the number of ways to arrange the men and woman on a stage with $12$ positions (2 rows and 6 columns) so the men are in the back and the women in the front.Selecting which people are going to be wearing hats and which are not and finally selecting which columns are going to have the lights pointed at