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There are 4 quarters and 3 dimes placed at random in a line.

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Manager
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There are 4 quarters and 3 dimes placed at random in a line. [#permalink] New post 15 Oct 2006, 10:14
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There are 4 quarters and 3 dimes placed at random in a line. The probability that the both extreme coins are dimes is

a) 1/4
b) 1/3
c) 1/7
d) 1/12
e) 1/2
Senior Manager
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 [#permalink] New post 15 Oct 2006, 10:26
I think it is 1 / 7

Explanation –

4 quarters are identical and 3 dimes are identical
4 quarters and 3 dimes can be placed in (4 + 3) ! / ( 4! * 3 !) ways = 35 ways

Consider extreme 2 corners are 2 dimes. Then the remaining coins are 4 quarters and 1 dimes.
4 quarters and 1 dime can be arranged in (4 + 1) ! / ( 4! * 1 !) = 5

So the probability is = (Possible 5 cases) / (total cases 35) = 1/7
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Re: Quarters n Dimes [#permalink] New post 15 Oct 2006, 10:28
yeah, I also get 1/7.
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 [#permalink] New post 15 Oct 2006, 11:00
1/7 too

D _ _ _ _ _ D

3P2 * 5P5
------------
7P7
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 [#permalink] New post 15 Oct 2006, 22:37
i think the qus is simply asking how to choose 2 quarters out of a total of 7 coins...and not about how other coins will be placed...

what u think??
  [#permalink] 15 Oct 2006, 22:37
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There are 4 quarters and 3 dimes placed at random in a line.

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