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Twenty five of King Arthur's knights are seated at their customary round table. Three of them are chosen - all choices of three being equally likely - and are sent off to slay a troublesome dragon.  What is the probability that at least two of the three had been sitting next to each other?

 Aug 4, 2020
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We have C(25,3)=2300 possible ways and there are C(3,1)*12=3*12=36 ways so the probability that at least two of the three had been sitting next to each other is \(\dfrac{36}{2300}=\dfrac9{575}\)

 Aug 4, 2020

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