A dance class consists of $22$ students, of which $10$ are women and $12$ are men. If $5$ men and $5$ women are to be chosen and then paired off, how many results are possible?
According to me, the number of results possible is:
Answer given :
Shouldn't be there $2$ options in each pair i.e ordering between men and women for $5$ such group, making it $5!$? Why is the answer not leaving $5!$? Are they not considering order? And if the order is important, is my answer correct in this case?