p and c

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p and c

Questions & Discussions » Maths Questions


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Replies : 2	Last Replied :11/09/2009

Views : 155	Go to last reply

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18/07/2009 17:58:40

Title: p and c

Status : Answered but not Reviewed

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Shivam Rastogi

Joined: 15/08/2008

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the no. of n-bit(0&1) strings having exactly k 0's and no 2 0's consecutive is_________

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11/09/2009 02:00:44

Title: p and c

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sahil sharma

Joined: 17/06/2009

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let the no of 1's be = a
no of 0's = k
total permutations are (a+k)!/(a!*k!) - *
now consider the case where at least two 0's are conseq. then, total elements are (assuming 00 to be 1 element) =(a+k-1) total permutations are
(a+k-1)!/(a!* [k-1]!) - **
subtracting ** from * gives our answer

PS: plz tell me if i'm wrong!!

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11/09/2009 02:07:22

Title: p and c

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sahil sharma

Joined: 17/06/2009

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oh ..one small mistake...we multiple ** by k!/(2!&[k-2]!)
here this denotes the no. of ways of choosing 2 0's out of k 0's...

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