How many ways can the 60 people from 20 countries be seated so that each president are sitting consecutively? The full question is: How many ways can the 60 people from 20 countries be seated **around a table** so that each president, vice president, and poet laureate are sitting consecutively? The answer I come up with is : (19!)*6 19! = the number of ways to arrange each country in the table = (20-1)! 6 = the number of ways to arrange the seat of three people in each country which are: [P,V,L] [P,L,V] [V,P,L] [V,L,P] [L,V,P] [L,P,V] But I'm an not sure if whether or not this answer is correct. Please help me. Thank you

Consider, each triplet of [P, V, L] as one bundle. So, there are total $20$ bundles.

Now, arranging these $20$ bundles on a circular table requires $(20-1)!$

Also, these bundles can be arranged internally which requires $3!$

Thus, the answer will be $$19! * (3!)^{20}$$