A box contains two white balls, three black balls and four red balls. In how many ways can three balls be drawn from the box, if atleast one black ball is to be included in the draw?

Question

Infinity Learn · Accepted Answer

A selection of $$3$$ balls so as to include atleast one black ball, can be made in the following $$3$$ mutually exclusive $$ways(i)$$ The number of ways in which $$1$$ black balls and $$2$$ others are $$selected=3C1$$×$$6C2=3$$×$$15=45(ii)$$ The number of ways in which $$2$$ black balls and $$1$$ other are selected $$=3C2$$×$$6C1=3$$×$$6=18(iii)$$ The number of ways in which $$3$$ black balls and no other are selected $$=3C3=1$$.'. Total numbers of ways $$=$$ $$45$$ $$+$$ $$18$$ $$+$$ $$1$$ $$=$$ $$64$$

A box contains two white balls, three black balls and four red balls. In how many ways can three balls be drawn from the box, if atleast one black ball is to be included in the draw?

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