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

April 9, 2022

by Ezee_Notes

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Maths Problems

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

(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