A probability problem by Vrks Sai

Probability Level 3

A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw?


The answer is 64.

Vrks Sai by Vrks Sai , 24, India

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2 solutions

Vrks Sai
Mar 14, 2014

We may have(1 black and 2 non-black) or (2 black and 1 non-black) or (3 black).

Required number of ways = (3C1 x 6C2) + (3C2 x 6C1) + (3C3) = 3 x 6 x 5 + 3 x 2 x 6 + 1 2 x 1 2 x 1 = (45 + 18 + 1) = 64.

4 Helpful 0 Interesting 0 Brilliant 0 Confused

hey ...why cant we say 8C2 ...select one black ball...and any other will do??

Mick Jagger - 7 years, 2 months ago

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because we don't know which black is always selected...........

Mayank Holmes - 7 years, 2 months ago

you should specify that the balls are differents( like numbered for example) otherwise i think your result is not correct..for example you can have 1black ball with two red balls in two ways but if the balls are not different is just one configuration..

guido barta - 5 years, 6 months ago
Akash Shah
Mar 31, 2014

No. of ways to select at least 1 black = No. of ways of Selecting 3 balls from total 9 balls - No. of ways of selecting all the three from 6 non-black balls =9C3 - 6C3=84 - 20= 64.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

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