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# The letters of word LABOUR ARE permuted in all possible ways and the

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Intern
Joined: 10 Jan 2011
Posts: 14
Location: India
Schools: ISB, IIM-A
WE 1: 4 yrs in finance
The letters of word LABOUR ARE permuted in all possible ways and the  [#permalink]

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19 Jun 2011, 18:49
4
00:00

Difficulty:

25% (medium)

Question Stats:

74% (01:52) correct 26% (02:47) wrong based on 52 sessions

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The letters of word LABOUR ARE permuted in all possible ways and the words thus formed are arranged in alphabetical order, then wht is the rank of word labour?

a) 400
b) 242
c) 152
d) 340

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Rahul

Manager
Joined: 24 Nov 2010
Posts: 176
Location: United States (CA)
Concentration: Technology, Entrepreneurship
Schools: Ross '15, Duke '15
Re: The letters of word LABOUR ARE permuted in all possible ways and the  [#permalink]

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19 Jun 2011, 20:40
1
L A B O U R
_ _ _ _ _

There are 6 letters in all. if all permutations are arranged alphabetically, then all words starting with A and B will be before LABOUR.
Words starting with A = A 5*4*3*2*1 = 120(First letter can be filled in one way (A), 2nd letter can be filled in 5 ways.. and so on). Note that here arrangement matters and there are no repeated letters that we need to worry about.

Similarly, all words starting with B = B 5*4*3*2*1 = 120

So till now we have 120 + 120 = 240 words in alphabetical order before words starting with L.

the 241st word will be LABORU and the 242nd word will be LABOUR.

Hence Ans = B
Director
Joined: 27 May 2012
Posts: 683
Re: The letters of word LABOUR ARE permuted in all possible ways and the  [#permalink]

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08 Sep 2018, 03:13
ITMRAHUL wrote:
The letters of word LABOUR ARE permuted in all possible ways and the words thus formed are arranged in alphabetical order, then wht is the rank of word labour?

a) 400
b) 242
c) 152
d) 340

Not able to understand this question, can body provide a detailed solution to this question. Thank you.
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- Stne

Manager
Joined: 18 Apr 2018
Posts: 97
Re: The letters of word LABOUR ARE permuted in all possible ways and the  [#permalink]

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10 Dec 2018, 23:10
I don't understand the solution as well. Shouldn't the words after those starting with A and B be that starting with O, please can an expert share a detailed explanation. Thanks

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Re: The letters of word LABOUR ARE permuted in all possible ways and the   [#permalink] 10 Dec 2018, 23:10
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