The number of ways in which the letters of the word TRIANGLE can be arranged such that two vowels do not occur together is

The number of ways in which the letters of the word 'ARRANGE' can be arranged so that two A's are together is

The number of ways in which letter of the word '"ARRANGE"' can be arranged, such that no two R's are together, is

The number of ways in which the letters of the word ARRANGE be arranged so that (i) the two R's are never together, (ii) the two A's are together but not two R's. (iii) neither two A's nor two R's are together.

Number of ways in which the letters of the word RIANBOW be arranged such that N and B are together is

The number of ways in which the letters of the word PESSIMISTIC can be arranged so that no two S's are together, no of two I's are together and letters S and I are never together is