In how many ways can the letters of the word PLANTAIN be arranged so that the two A do not come together?

In how many ways can the letters of the word ARRANGE' be arranged

In how many ways can the letters of the word 'PARALLEL' be arranged so that all L' s do not come together ?

In how many ways can the letters of the word 'GLOOMY' be arranged so that the two O's should not be together ?

In how many other ways can the letters of the word MULTIPLE be arranged