Chinki has some ‘fraction bars'. The longest bar is the red one (R). She has some purple bars (P) that are 3⁄4 of the length of the red one, some yellow bars (Y) that are 1/2 of the length of the red one and some green bars (G) that are 1⁄4 of the length of the red one. Chinki wants to arrange 2 or more different bars end to end to create a bar equal in length to the red bar. 3 DIFFERENT WAYS of doing it are shown:

(Note that GGY and YGG are two DIFFERENT arrangements.)

In all, how many different arrangements like these are possible?