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 neighbouring his car are empty is

Question : 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 neighbouring his car are empty is

(A) \dfrac{\left( r-1\right) !}{\left( N-1\right) !}

(B) \dfrac{\left( r-1\right) !\left( N-r\right) !}{\left( N-1\right) !}

(C) \dfrac{\left( N- r \right) \left( N- r -1\right) }{\left( N+1\right) \left( N+2\right) }

(D) \dfrac{N-r C_{2}}{N-1C_{2}}

Answer : option (D)

Solution :

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 neighbouring his car are empty is
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