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# Permutation and Combination

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Intern
Joined: 17 Sep 2005
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Location: Delhi
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Permutation and Combination [#permalink]  19 Sep 2005, 22:29
Hi

Help me with the P&C question below, tell simple way. Tell me links where I can find more of P&C stuff.

In how many ways can the letters of the word ABACUS be
rearranged such that the vowels always appear together?

A. 6!/2!
B. 3!*3!
C. 4!/2!
D. 4! *3!/2!
E. 3!*3!/2

Thanks
Director
Joined: 13 Nov 2003
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Location: BULGARIA
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ABACUS has 6 letters, 3 vowels and 3 consonants .Take all the vowels as one unit then u have 4 elements- each of the consonants and a group of 3 vowels. This can be ordered in 4! ways. But don't forget that the group of 3 vowels can have 3! orderings within the group. Or we have 4!x3! and finally cause u have 2-A's you need to divide the whole product by2!, or your ans should be (4!x3!)/2! or option D)
Senior Manager
Joined: 27 Aug 2005
Posts: 332
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Same here, intuitively. 72 is the answer.

There are 4 places where the string of 3 vowels can appear:
VVVCCC
CVVVCC
CCVVVC
CCCVVV

The string of vowels can be arranged in 3 ways (because two of the letters are identical As):
AAU
AUA
UAA

The string of consonants can be arranged in 6 ways (because the letters are all different):
BCS
BSC
CBS
CSB
SCB
SBC

4x6x3 = 72 = 4! *3!/2! or D.
Intern
Joined: 19 Aug 2005
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D.. same explanation as others

For P&Cs i borrowed a book called Probability without tears from my local library and got help. i guess if u have time u can try gettin a book too
Intern
Joined: 17 Sep 2005
Posts: 7
Location: Delhi
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Kudos [?]: 0 [0], given: 0

BG wrote:
ABACUS has 6 letters, 3 vowels and 3 consonants .Take all the vowels as one unit then u have 4 elements- each of the consonants and a group of 3 vowels. This can be ordered in 4! ways. But don't forget that the group of 3 vowels can have 3! orderings within the group. Or we have 4!x3! and finally cause u have 2-A's you need to divide the whole product by2!, or your ans should be (4!x3!)/2! or option D)

Thank you very much for the simple explanation
Intern
Joined: 17 Sep 2005
Posts: 7
Location: Delhi
Followers: 0

Kudos [?]: 0 [0], given: 0

coffeeloverfreak wrote:
Same here, intuitively. 72 is the answer.

There are 4 places where the string of 3 vowels can appear:
VVVCCC
CVVVCC
CCVVVC
CCCVVV

The string of vowels can be arranged in 3 ways (because two of the letters are identical As):
AAU
AUA
UAA

The string of consonants can be arranged in 6 ways (because the letters are all different):
BCS
BSC
CBS
CSB
SCB
SBC

4x6x3 = 72 = 4! *3!/2! or D.

Thank you very much.
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