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Number of ways the letters of word LETTER can be arranged such that vowels do not occur together

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

Q. Find the number of different 8 letter arrangements that can be made from the letters of the word "DAUGHTER " so that

(A)

All vowels occur together

(B)

All vowels do not occur together

Q. Find the number of different

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letter arrangements that can be made from the letters of the word

D A U G H T E R

(i)

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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

1) all vowels occur together

2) all vowels do not occur together.

Q. Find the number of different 8-letter arrangement that can be made from the letters of the word DAUGHTER so that(i)all the vowels occur together(ii)all the vowels do not occur together

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