Find the number of different 8-letter arrangements that can be made from the letters of the word...

Question From - NCERT Maths Class 11 Chapter 7 SOLVED EXAMPLES Question – 14 PERMUTATIONS AND COMBINATIONS CBSE, RBSE, UP, MP, BIHAR BOARD

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

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Related Questions & Solutions:

1. Find the number of 4 letter words, with or without meaning, which can be formed out of the letters of the word ROSE, where the repetition of the letters is not allowed....

2. Given 4 flags of different colours, how many different signals can be generated, if a signal requires the use of 2 flags one below the other?...

3. How many 2 digit even numbers can be formed from the digits 1, 2, 3, 4, 5 if the digits can be repeated?...

4. Find the number of different signals that can be generated by arranging at least 2 flags in order (one below the other) on a vertical staff, if five different flags are available....

5. Evaluate (i) 5! (ii) 7! (iii) 7! 5!...

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[rakeshkaushik]

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[krishshiv]

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[aora]

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[contagiousscorpio]

But logically the answer is coming out - 36000 the way you did sir

[shabnamara]

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[dkb]

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[huyanhle]

Wrong answer for part (ii) as you just have minus {A.U.E} only. How about when {A.U}, {A.E}, {U.E}....

That is why correct answer for part (ii) is = 5! X 6C3 X 3! = 5! X 6P3 = 14400