20 PEOPLE , OF WHICH 10 ARE DOCTORS AND 10 ARE ENGINEERS GO IN A MEETING , WHEN THEY COME OUT , THEY FIND THEIR JACKETS JUMBLED UP.WHATS THE PROBABILITY THAT NO ENGINEER GETS HIS ORIGINAL JACKET.

there are 20 coats, so the probability of the first engineer getting his coat wrong is 19/20, as there is only a 1/20 chance of getting the coat correct. the probability of the 2^nd engineer getting his coat wrong is 18/19 as he has 19 coats to chose from as the first engineer has already taken one coat. similarly the probality of the 10^th engineer getting his coat wrong is 10/11. 

19/20*18/19*17/18*--------------*11/12*10/11 = 1/2