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# G, D, I, I, F form strings such as GDIIF OR DGIFI, how many

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CEO
Joined: 15 Aug 2003
Posts: 3467
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Kudos [?]: 718 [0], given: 781

G, D, I, I, F form strings such as GDIIF OR DGIFI, how many [#permalink]  09 Oct 2003, 14:44
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G, D, I, I, F form strings such as GDIIF OR DGIFI, how many strings there are if there is at least one letter between the two I's?

Thanks
Praetorian
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Joined: 29 Aug 2003
Posts: 49
Location: Detroit, MI
Followers: 0

Kudos [?]: 2 [0], given: 0

Re: PS : Counting Methods ..Strings [#permalink]  09 Oct 2003, 15:53
praetorian123 wrote:
G, D, I, I, F form strings such as GDIIF OR DGIFI, how many strings there are if there is at least one letter between the two I's?

Thanks
Praetorian

The number of combinations using all the letters given = 5!/2! (2! for the repeating I's)

Subtract this from the combinations where I's appear together.

To get this, consider the 2 I's together to be a single letter. That way we have only 4 characters.

These can be arranged in 4! ways. In 4! combinations, the 2 I's appear together.

So, answer = 5!/2! - 4! = 60 - 24 = 36.

Amar.
Re: PS : Counting Methods ..Strings   [#permalink] 09 Oct 2003, 15:53
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