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Algebra

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Joined:	23 Dec 2006
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16 Jan 2007 12:06:15 IST

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A problem worth 100 salutes

None

There are 14 intermediate stations between C & B. A train starts from C towards B and stops at exactly 3 of the intermediate stations. Find the no. of ways in which this can happen provided that no two of the haulting stations are consecutive?? ( haulting station means the intermediate station where the train has stopped)

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malay

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Joined: 18 Dec 2006

Posts: 146

16 Jan 2007 12:29:35 IST

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let X,Y,Z be the stopping stations
a be the no. of stations before X
b between X and Y
c between Y and Z
d after Z

as required
a and d are non-negative integers
b and c are positive integers
and a+b+c+d=11
let a+1=e
d+1=f
hence
b+c+e+f=13
the no. of positive ineger solution of this equation gives the no. of ways

malay

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Joined: 18 Dec 2006

Posts: 146

16 Jan 2007 12:32:31 IST

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if above reasoning is right and my calculation also,
the answer is C(12,9) or 220

Marshall Eriksen

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Joined: 24 Dec 2006

Posts: 1312

16 Jan 2007 13:38:39 IST

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I Agree with guy above me....i reached same answer...12C9

Titun

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Joined: 23 Dec 2006

Posts: 374

16 Jan 2007 14:08:26 IST

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Thanks, Malay ur answer of 220 is correct. So, take a salute from me !!!

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