Question

How many different words can be formed by arranging letters of work 'ARRANGE' if neither two R's nor two A's occur together?

Answer 1

Total number of arrangements possible $=\frac{7!}{2!2!}=1260$

Total number of arrangements in which 2R's are together $=\frac{6!}{2!}=360$

Total number of arrangements in which 2A's are together $=\frac{6!}{2!}=360$

Total number of arrangements in which 2A's as well as 2R's are together $=5!=120$

Therefore total number of arrangements in which neither 2A's nor 2R's are together $=1260-360-360+120=660$