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April 1, 2015

Posted by **Anamika** on Thursday, December 6, 2012 at 1:37am.

(a) In how many of these anagrams none of the vowels come together.

(b) In how many of these anagrams do the vowels and the consonants occupy the same relative positions as in HINDUSTAN?

- maths-probability -
**Reiny**, Thursday, December 6, 2012 at 8:39amnumber of arrangements without restriction = 9!/2 = 181440 (There were 2 N's, so we divide by 2!)

We have 3 vowels, we don't want any 2 to be beside each other.

so consider the possible pairs.

IU IA UA UI AI AU , that is there are 6 of the, or P(3,2)

So if we consider a pair of vowels to be X , the number of ways for the vowels to be together is

8! (6)/2 = 120960

(notice that would include the cases where the 3 vowels are together

e.g.**IA**HNDUSTN

and**IAU**HNDSTN

number of ways for the vowels to be apart

= 181440 - 120960 = 60480

b) The relative position of vowels and consonants must remain the same, so we need

CVCCVCCVC , given 6 cosonants (2 the same) and 3 vowels

or 6x3x5x4x2x3x2x1x1/2! = 2160

check my arithmetic

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