A man parks his car among n cars standing in a row, his car not being parked at an end, on his return he finds that exactly m of the n cars are still there, probability that both the cars parked on tw

Question

A man parks his car among n cars standing in a row, his car not being parked at an end, on his return he finds that exactly m of the n cars are still there, probability that both the cars parked on two sides of his car ,have left is ( n − A ) ( n − B ) ( n − m ) ( n − m − 1 ) ​ then A + B is

TestHub · Accepted Answer

Number of ways in which remaining ′ m − 1 ′ cars can take their places (excluding the car of man) = n − 1 C m − 1 ​ No.of ways in which remaining ( m − 1 ) cars can take places keeping the two places on two sides of his car vacant = n − 3 C m − 1 ​ ​ Prob = n − 1 C m − 1 ​ n − 3 C m − 1 ​ ​ = ( n − 1 ) ( n − 2 ) ( n − m ) ( n − m − 1 ) ​ ​ ⇒ A = 1 ​ B = 2 ​ A + B = 3 ​

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