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There are 10 stations on a circular path...

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`

Text Solution

Verified by Experts

The correct Answer is:
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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