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the letters of the word 'SURITI' are written in all possible

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the letters of the word 'SURITI' are written in all possible [#permalink] New post 24 Jan 2013, 09:13
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The letters of the word 'SURITI' are written in all possible orders and these words are written in alphabetical order. Then what is the rank of the word 'SURITI'
A - 236
B - 245
C - 307
D - 315
E - 275

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Re: the letters of the word 'SURITI' are written in all possible [#permalink] New post 24 Jan 2013, 09:47
As a helpful hint for anyone trying to solve, this questions has many parts:

1) Identify the number of combinations that start with I
2) Identify the number of combinations that start with R
3) Identify the number of combinations that start with SI
4) Identify the number of combinations that start with SR
5) Identify the number of combinations that start with ST
6) Identify the number of combinations that start with SUI
7) Identify the number of combinations that start with SURII (This is just 1)
8) Add 1 to the sum of the list above.



As a hint for number 1, the number is (2 x 5 x 4 x 3 x 2)/2! or 120
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Re: the letters of the word 'SURITI' are written in all possible [#permalink] New post 24 Jan 2013, 11:00
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aalok26 wrote:
The letters of the word 'SURITI' are written in all possible orders and these words are written in alphabetical order. Then what is the rank of the word 'SURITI'
A - 236
B - 245
C - 307
D - 315
E - 275

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Total Number of Words = 6!/2! = 360 [(number of characters)/(repeating group )!]

After S, we have T and U.

Number of words starting with T = 5!/2! = 60
Number of words starting with U = 5!/2! = 60

So any word starting with S will have rank < 360 - 60(for Us) - 60(for Ts) = 240

Only option A < 240, so Answer is A.
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Re: the letters of the word 'SURITI' are written in all possible [#permalink] New post 24 Jan 2013, 11:03
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Very nice way of solving as well!
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Re: the letters of the word 'SURITI' are written in all possible   [#permalink] 24 Jan 2013, 11:03
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