2
Question
A car is parked among N cars standing in a row, but at either end. On his return, the owner finds that exactly r of the N places are still occupied. The probability that both the places neighboring his car are empty is
A car is parked among N cars standing in a row, but at either end. On his return, the owner finds that exactly r of the N places are still occupied. The probability that both the places neighboring his car are empty is
Open in App
Solution
The correct option is B N−3Cr−1N−1Cr−1
Finding r cars in N places means there are r−1 cars other that his own in N−1 places.
The number of way this is possible is N−1Cr−1.
But if the neighboring slots are empty, the r−1 cars must be parked in N−3 places,
which can be done in N−3Cr−1 ways.
Therefore the probability of the required event is N−3Cr−1N−1Cr−1
Finding r cars in N places means there are r−1 cars other that his own in N−1 places.
The number of way this is possible is N−1Cr−1.
But if the neighboring slots are empty, the r−1 cars must be parked in N−3 places,
which can be done in N−3Cr−1 ways.
Therefore the probability of the required event is N−3Cr−1N−1Cr−1
Suggest Corrections
0
Similar questions
View More
Join BYJU'S Learning Program
Explore more
Join BYJU'S Learning Program
