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# How many ways are possible to arrange five letters so that

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Senior Manager
Joined: 15 Aug 2004
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How many ways are possible to arrange five letters so that [#permalink]  29 Aug 2006, 01:49
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How many ways are possible to arrange five letters so that at least 2 letters are between two "R"?
Director
Joined: 13 Nov 2003
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[#permalink]  29 Aug 2006, 02:11
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
Senior Manager
Joined: 14 Jul 2006
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[#permalink]  29 Aug 2006, 10:01
Using the counting method
18

R32R1=6
3R21R=6
R321R=6
Manager
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These probability questions kill me!!! [#permalink]  29 Aug 2006, 10:23
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: These probability questions kill me!!! [#permalink]  30 Aug 2006, 07:30
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

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

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.

3*3P1= 18
Re: These probability questions kill me!!!   [#permalink] 30 Aug 2006, 07:30
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# How many ways are possible to arrange five letters so that

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