# Math Help - Permutations of people

1. ## Permutations of people

Hi all, I've got this question here... don't even know how to begin solving it.

There are 28 people from 7 countries; 4 people from each country. I'm required to put them in a line, so that each person will have at least one neighbour from the same country. How many such orderings exist?

Thus there are $3^7$ ways to choose the paring of all 28 people.
For any choice of parings, we have $(14!)$ ways to arrange these pairs into a line.
In each of those lines there are $2^{14}$ ways to arrange the couples.