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Question

There are 10 persons sitting around a circular table from which three persons are selected for the board of directors. The number of ways to select them such that no two persons are adjacent to each other is

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Solution

Let the number of required ways be r.
Number of ways to select 3 persons without restrictions = 10C3
Number of ways to select three members together = 10
Number of ways to select two members together and one member separately = 10×6C1
Then,
r=10C3(10+10×6C1)
r=50

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