A box contains 2 white balls, 3 black balls and 4 red balls. In how ma

1.	A box contains 2 white balls, 3 black balls and 4 red balls. In how manyways can 3 balls be drawn from the box, if at least one black ball is to beincluded in the draw?c)8子
Answer» The bag contains 2 White, 3 Black and 4 Red balls. So, total 9 balls are there in the bag; among them 3 are Black and 6 are non-Black balls. Three balls can randomly be drawn in (9C3) = 84 ways. 1 Black and 2 non-Black balls can be drawn in (3C1)(6C2) = 45 ways. 1 non-Black and 2 Black balls can be drawn in (6C1)(3C2) = 18 ways. 3 non-Black balls can be drawn in (3C3) = 1 way. So, three balls drawn in (45 + 18 + 1) = 64 ways will have at least one Black ball among the drawn ones. So, the probability of getting at least one Black ball among the three drawn = (64 / 84) = (16 / 21).

A box contains 2 white balls, 3 black balls and 4 red balls. In how manyways can 3 balls be drawn from the box, if at least one black ball is to beincluded in the draw?c)8子

Answer»

The bag contains 2 White, 3 Black and 4 Red balls.

So, total 9 balls are there in the bag; among them 3 are Black and 6 are non-Black balls.

Three balls can randomly be drawn in (9C3) = 84 ways.

1 Black and 2 non-Black balls can be drawn in (3C1)*(6C2) = 45 ways.

1 non-Black and 2 Black balls can be drawn in (6C1)*(3C2) = 18 ways.

3 non-Black balls can be drawn in (3C3) = 1 way.

So, three balls drawn in (45 + 18 + 1) = 64 ways will have at least one Black ball among the drawn ones.

So, the probability of getting at least one Black ball among the three drawn =

(64 / 84) = (16 / 21).