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A car is parked among N cars standing i...

A car is parked among `N` cars standing in a row, but not at either end. On his return, the owner finds that exactly `"r"` of the `N` places are still occupied. The probability that the places neighboring his car are empty is a.`((r-1)!)/((N-1)!)` b. `((r-1)!(N-r)!)/((N-1)!)` c. `((N-r)(N-r-1))/((N-1)(N+2))` d. `"^((N-r)C_2)/(.^(N-1)C_2)`

A

`((r-1)!)/((N-1)!)`

B

`((r-1)!(N-r)!)/((N-1)!)`

C

`((N-r)(N-r-1))/((N+1)(N+2))`

D

`(.^(N-r)C_(2))/(.^(N-1)C_(2))`

Text Solution

AI Generated Solution

To solve the problem, we need to find the probability that the places neighboring the owner's car are empty, given that there are `N` cars in total and `r` of the `N` places are still occupied. ### Step-by-Step Solution: 1. **Identify the Total Places**: The total number of places is `N`. Since the owner's car is not parked at either end, it can occupy any of the positions from 2 to N-1. 2. **Determine the Number of Occupied Places**: ...
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