Q.

There are 17 railway stations in a railway track between A and B. The train stops at 4 intermediate stations at random. Then the probability that at least two of these 4 stations are consecutive is

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a

227340

b

113340

c

197340

d

143340

answer is A.

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Detailed Solution

Train is to be stopped at 4 stations out of 17. 
Prob (At least two of the 4 stops are adjacent)
=1– prob ( No two of them are adjacent )
=1 nr+1Cr nCr where n=17,r=14=1 14C4 17C4=114.13.12.1117.16.15.14=1143340=197340

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