Asked by Katie
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?
Answers
Answered by
Alex
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
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
There are no AI answers yet. The ability to request AI answers is coming soon!