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

Question

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

Infinity Learn · Accepted Answer

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 $$isP(I)+P(II)+P(III)=$$ $$5C3$$×$$10C8$$ $$15C11+$$ $$5C4$$×$$10C7$$ $$15C11+$$ $$5C5$$×$$10C6$$ $$15C11=12601365=1213$$

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

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