a taxi cab company has 12 ambassadors and 8 fiats. If 5 of these taxi cabs are in workshop for repair, calculate the probability that i) 3 of them are ambassadors and 2 flats ii) all the 5 are of the same make

i) we use the concept of combination as below

( ( 12C3 ) * ( 8C2 ) ) / ( 20C5 ) = ( 220 * 28 )/ ( 15504 )

which yields 0.397316821 which is the required probability.

ii) we also use the concept of combination as below

( ( 12C3 ) * ( 8C0) ) / (20C5) + ( ( 12C0 ) * ( 8C5 ) ) / ( 20C5 )

which becomes

( 792(1) + 1(56) ) / ( 15504)

which yields

0.054695562 which is the required probability