Permutations of word MANIFOLD

Question

In how many ways can the letters of the word MANIFOLD be arranged so that the vowels are separated?

I tried total permutations in which vowels are together, which gives 36000 which was wrong.

You consistently ask low quality questions. See the help centre for tips. — Shaun, Aug 28 '17 at 07:49

score 0 · Accepted Answer · answered Aug 28 '17 at 07:35

0

All letters are distinct, so there are $8!$ permutations. This count both good and bad ones.

Consider two of the vowels as one letter ($3!/1!$ cases). Each of the cases constitutes $7!$ bad permutations.

Consider three vowels as on letter ($3!$ cases). Each of the cases constitute $6!$ bad permutations which were however counted twice by the $3! 7!$ above, so these bust be added.

I.e. $8!-3!7!+3!6!$

answered Aug 28 '17 at 07:35

Coolwater

1,292

@GirishArora I get 14400, what do you think is the answer?! – Coolwater Aug 28 '17 at 07:42
8! - (3!7! + 3!6!) Does not sums up to 14400...however (8! -3!7!) + 3!6! = 14400 which is correct. I used BODMAS before. – Techievent.in Aug 28 '17 at 07:47
@GirishArora BODMAS is really BO(DM)(AS) (assuming "O" has something to do with exponents), where the two pairs in brackets have equal priority. In the case of DM, it is ambiguous, and in the case of AS, it goes left-to-right. – Arthur Aug 28 '17 at 09:01
@arthur thanks for reminding me that – Techievent.in Aug 28 '17 at 09:11
@pritt balagopal i mentioned in the comment that answer is right – Techievent.in Aug 28 '17 at 09:12

Permutations of word MANIFOLD

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