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Previous Year Question (PYQs)



20 persons are sitting in a particular arrangement around a circular table.
3 persons are to be selected for leaders.
The number of ways of selection of 3 persons such that no 2 were sitting adjacent to each other is:





Solution

For circular arrangement, required formula: $\text{Ways} = \dfrac{n}{n - r} \binom{n - r}{r}$ Substitute $n=20, r=3$ $\Rightarrow \text{Ways} = \dfrac{20}{17} \binom{17}{3} = 20 \times 68 / 17 = 800$


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