Grade 12th PassAlgebra

A car is parked by a driver amongst 25 cars in a row, not at either end. When he returns he finds that 10 places are empty. The probability that both the neighbouring places of drivers car are vacant, is???Pls explain how???

Aditi Bhatnagar

14 Years agoGrade 12th Pass

2 Answers

jitender lakhanpal

14 Years ago

Dear,

answer is C(23,8) / C (25,10)

for solution

please find the attachment

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jitender

Kunal Upadhyay

8 Years ago

Since the owner finds on return that exactly 10 of the 25 Places(inckuding owner’s car) are occupied, the exhaustive no. of cases for such an arrangement is ^(25-1)C(10-1) = ²⁴C₉[ since the remaining 9 cars to be parked in remaining 24 places]

Let E denote the event that both neighbouring places to owner’s car are empty. This require thr remaning 9 cars to be parked in remainig (25-3)=22 Places and hence the no of cases favourabke to E is ²²C9 . Hence,

P(E) = ²²C₉/ ²⁴C₉ = 35/92 = 0.38043 Ans.