Q.11. In how many ways can the letters of the word PERMUTATIONS be arranged if the
(ii) vowels are all together?
There are 5 vowels in word PERMUTATIONS and each appears once.
Since all 5 vowels are to occur together so can be treated as 1 object.
The single object with the remaining 7 objects will be 8 objects.
The 8 objects in which 2 T's repeat can be arranged as
These 5 vowels can also be arranged in ways.
Hence, using the multiplication principle, the required number of arrangements are