A cricket club has 15 members, of whom only 5 can  bowl. If the names of 15 members are put into a box and 11 are drawn at random, then the probability of getting an eleven containing at least 3 bowlers is

The total number of ways of choosing 11 players out of 15 is  15C11 A team of 1l players containing at least 3 bowlers can be chosen in the following mutually exclusive ways: (I) Three bowlers out of 5 bowlers and 8 other players out of the remaining 10 players. (II) Four bowlers out of 5 bowlers and 7 other players out of the remaining 10 players. (III) Five bowlers out of 5 bowlers and 6 other players out of the remaining 10 players. So, required probability isP(I)+P(II)+P(III)= 5C3×10C8 15C11+ 5C4×10C7 15C11+ 5C5×10C6 15C11=12601365=1213