Four distinguishable particles move freely in a room divided into octants (there are no actual partitions). Let the basic states be given by specifying the octant in which each particle is located.

(a) Give an example of a macrostate for this system.

(b) How many basic states are there?

(c) The door to this room is opened, allowing the particles to move into an adjacent, identical room, also divided into octants. Now that the amount of space that can be occupied has been doubled, by what factor has the number of basic states increased?