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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 at least one black ball is to be included in the draw?

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 at least one black ball is to be included in the draw?

Grade:upto college level

1 Answers

Navjyot Kalra
askIITians Faculty 654 Points
9 years ago
Hello Student,
Please find the answer to your question
Number of ways drawing at least one black ball = 1 black and 2 other or 2 black and 1 other or 3 black
= 3 C1 x 6 C2 + 3 C2 x 6 C1 + 3 C3 = 3 x 15 + 3 x 6 + 1
= 45 + 18 + 1 = 64
ALTERNATE SOLUTION:
Number of ways drawing at least one black ball
= Total ways No. of ways of drawing no black ball
= 9 C3 – 6 C3 = 84 – 20 = 64

Thanks
navjot kalra
askIITians Faculty

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