Find the number of different 8-letter ar...

Find the number of different 8-letter arrangements that can be made from the letters of the word DAUGHTER so that
all vowels do not occur together.

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Find the number of different 8-letter arrangements that can be made from the letters of the word, 'DAUGHTER' so that: All vowels are occur together.

Find the number of different 8-letter arrangements that can be made from the letters of the word DAUGHTER so that all vowels occur together.

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In how many ways can the letters of the word 'ARRANGE' be arranged such that two A's do not occur together?

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