A box contains two white balls, three black balls and four red balls. Balls of the same colour are distinct. The number of ways in which three balls can be drawn from the box if atleast one black ball is to be included in the draw, is

32

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64

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128

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None of these

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Solution

The correct option is B $64$
The number of ways of selecting $3$ balls out of total $9 (2$ white, $3$ black, $4$ red balls $)$ is
$^{9} C_{3} = \frac{9 \times 8 \times 7}{6} = 84$
The number of ways of selecting $3$ balls out of non-black six balls is
$^{6} C_{3} = \frac{6 \times 8 \times 4}{3 \times 2 \times 1} = 20$
The desired number $= 84 - 20 = 64$

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A box contains two white balls, three black balls and four red balls. Balls of the same colour are distinct. The number of ways in which three balls can be drawn from the box if atleast one black ball is to be included in the draw, is

The correct option is B 64The number of ways of selecting 3 balls out of total 9(2 white, 3 black, 4 red balls) is 9C3=9×8×76=84The number of ways of selecting 3 balls out of non-black six balls is 6C3=6×8×43×2×1=20The desired number =84−20=64