A box contains two white balls, three black balls and four red balls. No. of ways can three balls be drawn from the box if at least one black ball is to be included in the draw is

129

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84

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64

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Solution

The correct option is C $64$
At least one black ball can be drawn in the following ways:
(i) one black and two other colour balls
(ii) two black and one other colour balls
(iii) all the three black balls
$∴$ The required number of ways is
$^{3} C_{1} \times^{6} C_{2} +^{3} C_{2} \times^{6} C_{1} +^{3} C_{3} = 64.$

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A box contains two white balls, three black balls and four red balls. No. of ways can three balls be drawn from the box if at least one black ball is to be included in the draw is

The correct option is C 64At least one black ball can be drawn in the following ways:(i) one black and two other colour balls(ii) two black and one other colour balls(iii) all the three black balls∴ The required number of ways is3C1×6C2+3C2×6C1+3C3=64.