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rc1979
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If you have the letters LOCAL, how many words can you form 17 Mar 2005, 10:07
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If you have the letters LOCAL, how many words can you form where there is at least one space between the Ls?



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ketanm
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If you have the letters LOCAL, how many words can you form 17 Mar 2005, 10:34
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rc1979
If you have the letters LOCAL, how many words can you form where there is at least one space between the Ls?
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First without considering any conditions, the total arrangements for the word LOCAL is 5!/2 (divided by 2!, since there are two letters same)

Consider the both LL as a group letter, now there will be four letters, which can be arranged in 4! ways.

Hence number of words where there is atleast one space between L's
= [ (5!/2) - 4!] = 36

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kapslock
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If you have the letters LOCAL, how many words can you form 17 Mar 2005, 10:45
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That's what I'd go for too.

5!/2 - 4!.

This is easy since the question read at least one space (alphabet) between the two Ls.

Try the variation of this question of finding the permutations with exactly 1 space (alphabet) between the two Ls.

Wud post my answer in a while.
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kapslock
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If you have the letters LOCAL, how many words can you form 17 Mar 2005, 10:54
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kapslock
That's what I'd go for too.

5!/2 - 4!.

This is easy since the question read at least one space (alphabet) between the two Ls.

Try the variation of this question of finding the permutations with exactly 1 space (alphabet) between the two Ls.

Wud post my answer in a while.
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Two ways of approaching this problem:

1. Consider L X L as a group, where X can be O, C or A.

Thus the variations are (L X L) Y Y where Y Y are the remaining characters.
For one value of X, the possible permutations are 3!. (Two Ys and one LXL).
For all possible three values of X, the possible permutations = 3 * 3! = 18

2. Consider the positions

L _ L _ _ - 3 positions, 3! variations possible
_ L _ L _ - 3 positions, 3! variations possible
_ _ L _ L - 3 positions, 3! variations possible

Total = 3 * 3!
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If you have the letters LOCAL, how many words can you form 17 Mar 2005, 17:22
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Nice explanation Ketan ... Keep it up
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vprabhala
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If you have the letters LOCAL, how many words can you form 17 Mar 2005, 18:10
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5! number of total words
as we have 2 L's
5!/2.
now we will try to find out in how many ways we can do LL's together. considering them as 1 unit. we can do it 4! ways.

5!/2-4! gives us the number of words without the LL's together..
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If you have the letters LOCAL, how many words can you form 18 Mar 2005, 03:31
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(5c2-4c1)*3! or 5!/2! - (4c1*3!) or logic I =>

_ _ _ _ _ => five spaces
L L _ _ _ => 1 way
_ L L _ _ => 1 way
_ _ L L _ => 1 way
_ _ _ L L => 1 way

=> 4 ways where LL are togther => multiply it by 3! => 24 => substract it from the total ways => 5!/2! - 24 = 36 or logic II =>

_ _ _ _ _ => five spaces
L _ _ _ L => 1 way
L _ _ L _ => 1 way
L _ L _ _ => 1 way
_ L _ L _ => 1 way
_ L _ _ L => 1 way
_ _ _ L L => 1 way

=> 6 ways where LL are NOT together => multiply it by 3! => 36

many ways to rome :-D



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