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20 persons are sitting in a particular arrangement around a circular table. Three persons are to be selected for leaders. The number of ways of selection of three persons such that no two were sitting adjacent to each other is

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a

600

b

900

c

800

d

none of these

detailed solution

Correct option is C

The total number of ways of selection without restriction is 20C3.The number of ways of selection when two are adjacent is 20×16C1. The number of ways of selection when all the three are adjacent is 20 . The required number of ways is 20C3−20×16−20=20×19×186−20×16−20=20[57−16−1]=20×40=800

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