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How many ways are possible to arrange five letters so that

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sumitsarkar82
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How many ways are possible to arrange five letters so that [#permalink] New post   29 Aug 2006, 02:49
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How many ways are possible to arrange five letters so that at least 2 letters are between two "R"?



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Re: How many ways are possible to arrange five letters so that [#permalink] New post   29 Aug 2006, 03:11
I will give it a try.

Alphabet, the english one, has 26 letters. Remove R , 25 remain. Now-RXXR and RXXXR or 25*24 +25*24*23.

THis is without repetition
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Re: How many ways are possible to arrange five letters so that [#permalink] New post   29 Aug 2006, 11:01
Using the counting method
18

R32R1=6
3R21R=6
R321R=6
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Re: How many ways are possible to arrange five letters so that [#permalink] New post   29 Aug 2006, 11:23
Okie here we go:

5 letters, so that at least two are between two Rs.
So we have:

1. RXXRX
2. XRXXR
3. RXXXR
where X can be any letter of the alphabet (assuming, including R!)

= 3*26C3
= 15600.

MG
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Re: How many ways are possible to arrange five letters so that [#permalink] New post   30 Aug 2006, 08:30
mikki0000 wrote:
Okie here we go:

5 letters, so that at least two are between two Rs.
So we have:

1. RXXRX
2. XRXXR
3. RXXXR
where X can be any letter of the alphabet (assuming, including R!)

= 3*26C3
= 15600.

MG

:shock:

That's really going into the problem "Jamacian me Crazy!" :wink:

Looks like Apollo nailed it.

R is the same letter, so we can only shift it in three possible ways to leave at least a gap of two spaces in between.

As for the other three letters, the stem didn't specify that they had to be English letters. :wink:

3*3P1= 18



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Re: How many ways are possible to arrange five letters so that [#permalink]
30 Aug 2006, 08:30
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