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How to approach the question CHAOS .


What should be approach for the question CHAOS

asked 04 Nov '15, 14:08

docodon's gravatar image

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edited 05 Nov '15, 14:40

N = 14 M = 2

_ X1 _ _ X2 _ _X3 _ _

here Xi denotes chaotic cities.

let C denotes no of cities between particular consecutive chaotic city. The order in which cities become chaotic range from 1 to N-M thus we have to find no of ways of selecting C orders out of N-M = combination(N-M,C); once order has been selected ,cities present on these order will permute among them self. e.g. there are 3 cities between X1 & X2 let we numbered it as 1,2 & 3. no of ways of arrangement are:(because of constraint of chaosing) 1 2 3

1 3 2

3 1 2

3 2 1

= 4

we can find for any n consecutive as: 2^(n-1) //22....(no of candidate for ith position of selected order ) 2...*1

thus number of ways of order cities between Xi & Xi+1 = comb(N-M,C) * 2^(C-1)

after set,no of available orders are :N-M-C

do this for all cities between consecutive chaotic cities and multiply them. find no of ways of order cities(p) before 1st chaotic city as:comb(remaining orders,p) and multiply it. after multiplication you will get answer.

feel free to ask any question:)


answered 06 Nov '15, 21:38

anil0004's gravatar image

accept rate: 50%

crystal clear explanation !! thanks buddy :)

(06 Nov '15, 23:03) docodon4★

answered 05 Nov '15, 15:51

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answered 19 May '17, 16:36

diksha12345's gravatar image

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question asked: 04 Nov '15, 14:08

question was seen: 1,232 times

last updated: 19 May '17, 16:36