Find the number of distinct words formed from letters in the word 'MANAGEMENT'. How many of them have the two M,A,N,E's together.

Find the number of distinct words formed from letters in the word INDIAN. How many of them have the two N's together?

Find the number of different ways of arranging letters in the word ARRANGE. How many of these arrangement do not have the two R's nor A's together?

Find the number of ways of arranging letters of the word MATHEMATICAL. How many of these arrangements have all vowels together?

Find the number of different words that can be formed from the letters of the word 'TRIANGLE' so that no vowels are together.