# 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???

Let driver's car is parked at 2nd spot.

then two of its neighbour cars are empty out of 10 if, its right side is empty, and left side is empty and other 8 places  are empty out of balace 22 places .

so prob = 1/24*1/24* (22C8)/(24C10)....(1)

but there can be 23 such cases, as driver can park its car ineither of the  2nd, 3rd, 4th....or .24th spot (i.e. 23 ways) and in each of the case prob of its neighbour places empty will be as in (1), so

overall prob = 23*1/24*1/24* (22C8)/(24C10) = 5/768

Out of those 10 empty places, no of ways in which  both of its 'neighbour cars' are included = 2C2*22C

So prob = 2C2*22C/ 24 C10 =15/92

(though i am not svery ure of this answer)

but from a) above,  driver's car cab be parked in 23 ways, and in each case prob will be same as in (1)

So Prob = 23 * 2C2*23C8 / 25 C10

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 Let driver's car is parked at 2nd spot. then two of its neighbour cars are empty out of 10 if, its right side is empty, and left side is empty and other 8 places are empty out of balace 22places . so prob = 1/24*1/24* (22C8)/(24C10)....(1) but there can be 23 such cases, as driver can park its car ineitherof the 2nd, 3rd, 4th....or .24th spot (i.e. 23 ways) and in each of the case prob of its neighbour places empty will be as in (1), so overall prob = 23*1/24*1/24* (22C8)/(24C10) = 5/768
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