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 . A team of 11 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 is
P(I) + P(II) + P(III)