Three Canadians, 4 Americans, and 2 Mexicans attend a trade conference. In how many ways can they be seated in a row if the people of the same nationality are to be seated next to each other?

Answer 1

We calculate the number of ways each nationality can order their members. This is simple permutations.

Canadians: 3! = 6
Americans: 4! = 12
Mexicans: 2! = 2

However, we can also manipulate the order of our diplomats (i.e. Canada, America, Mexico v. Canada, Mexico, America).

Again since, there are 3 options, we can simply calculate a permutation, 3! = 6.

We now take the sum of the first part and multiply it by the second part.

(6 + 12 + 2) * 6 = 120