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Mathematics - Permutation & Combination Question with Solution | TestHub

MathematicsPermutation & CombinationCircular PermutationMedium2 minQB

MathematicsMediumsingle choice

There are 10 stations on a circular path. A train has to stop at 3 stations such that no two stations are adjacent. The number of such selections must be

Options:

Answer:

Solution:

Total selections $^{10} C_{3} = 120$

Number of selections in which 3 stations are adjacent = 10

Number of selections in which 2 stations are adjacent $= 6$

But there are 10 such pairs.

⇒ Total invalid selections $= 10 + 6 \times 10 = 70$

Stream:JEESubject:MathematicsTopic:Permutation & CombinationSubtopic:Circular Permutation

⏱ 2mℹ️ Source: QB

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