Hi Everyone, 1. The problem statement, all variables and given/known data If we are asked the number of ways 2n people can be divided into 2 groups of n members, can I first calculate the number of groups of n members that can be formed from 2n people and then calculate number of ways 2 groups can be selected from the number of groups formed above? i.e. can I write: number of groups possible=(2n)!/n!(2n-n)!=(2n)!/(n!)^2=k(suppose) ways 2 group possible=k!/2!(k-2)! And if I am further asked the same question with following addition: if each department must choose a president and a vice president, then can I multiply the number I got above by the number of ways a group can be formed with a vice president and a president. i.e. we will have n(n+1)/2 ways for selection of a president and (n(n+1)/2)^2 since we have two groups? i.e. (k!/2!(k-2)!)*(n(n+1)/2)^2 2. Relevant equations c(n k)=n!/k!(n-k)! 3. The attempt at a solution Included in Part A ThankYou. Sorry for this messy style.