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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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a

49920 and 36000

b

4320 and 36000

c

4420 and 36000

d

None of these

answer is B.

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Detailed Solution

Word = DAUGHTER
Total words = 8
Number of vowels = 3
No. of ways reasoning vowel = 3P3 = 3! = 6
Total no of ways so that all vowel are together = 3P3✕ 6P6= 6 ✕ 720 = 4320
All the vowels done to occur together
= total number of ways – all vowel occur together
= 8! – 4320 = 40320 – 4320 = 36000
Hence the number of ways all vowels are together all the vowel do to occur together and 4320 and 36000 respectively

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