An airline owns 3 types of plane Airbus Boeing and Embraer w

An airline owns 3 types of plane: Airbus, Boeing and Embraer, with 20 planes of each type. Find the probability that a random group of 20 planes will be void in at least one type.

Solution

We have 3 types of plane, with 20 planes of each type
Choosing a group of 20 planes in codition of one type must void will be = Group of 20 only in from Airbus, Boeing, Void Embraer OR Group of 20 only in from Boeing, Embraer , Void Airbus OR Group of 20 only in from Embraer,Airbus, Void Boeing

Group of 20 only in from Airbus, Boeing, Void Embraer = 40 C 20
Group of 20 only in from Boeing, Embraer , Void Airbus = 40 C 20
Group of 20 only in from Embraer,Airbus, Void Boeing = 40 C 20

Final Probability = (40 C 20 + 40 C 20 + 40 C 20 )/ 60 C 20 = (nCr(40,20)+nCr(40,20)+nCr(40,20))/nCr(60,20) = 0.000098653