Q14 of 64 Page 122

A box contains two white, three black 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.

[Hint: Required number of ways =3C1×6C2+3C2x 6C1+3C3.]

FORMULA:- (i)nCr


Number of ways drawing at least one black ball =


=( 1 black and 2 other )or( 2 black and 1 other )or (3 black)


3C1x6C2+3C2x6C1+3C3


=3×15+3×6+1


= 45 + 18 + 1


= 64


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