A car is parked by an owner amongst 25 cars in a row not at either end. In his return he finds that exactly 15 places are still occupied. The probability that both the neighbouring places are empty is

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It is given that 15 places are occupied. 14 other cars are parked no. of ways of selecting 14 places from 24 in $^{24} C_{14}$ ways. Excluding the neighbouring places there are 22 places in where 14 cars can be parked in $^{22} C_{14}$ ways.

$∴ P (E) = \frac{^{22} C _{14}}{^{24} C _{14}}$

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