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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: (A) `50` (B) `84` (C) `126` (D) `70`A. `50`B. `60`C. `70`D. `80` |
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Answer» Correct Answer - A `(a)` 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. `implies` Total invalid selections `=10+6xx10=70` |
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