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#mathematics
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#probability
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Four balls are simultaneously drawn from a bag containing three green balls and six blue balls ,Find out how many combinations of drawing are possible if;there are at least two green balls ?

Feb 15

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Feb 15

To find the number of combinations of drawing with at least two green balls, we need to consider two scenarios: drawing exactly two green balls and drawing three green balls.

1. Drawing exactly two green balls:

There are 3 green balls in the bag, so we can choose 2 green balls out of 3 in C(3, 2) = 3 ways.

The remaining 2 balls must be blue, and there are 6 blue balls in the bag, so we can choose 2 blue balls out of 6 in C(6, 2) = 15 ways.

Therefore, the number of combinations of drawing exactly two green balls is 3 * 15 = 45.

2. Drawing three green balls:

There are 3 green balls in the bag, so we can choose 3 green balls out of 3 in C(3, 3) = 1 way.

The remaining ball must be blue, and there are 6 blue balls in the bag, so we can choose 1 blue ball out of 6 in C(6, 1) = 6 ways.

Therefore, the number of combinations of drawing three green balls is 1 * 6 = 6.

In total, the number of combinations of drawing with at least two green balls is 45 + 6 = 51.

1. Drawing exactly two green balls:

There are 3 green balls in the bag, so we can choose 2 green balls out of 3 in C(3, 2) = 3 ways.

The remaining 2 balls must be blue, and there are 6 blue balls in the bag, so we can choose 2 blue balls out of 6 in C(6, 2) = 15 ways.

Therefore, the number of combinations of drawing exactly two green balls is 3 * 15 = 45.

2. Drawing three green balls:

There are 3 green balls in the bag, so we can choose 3 green balls out of 3 in C(3, 3) = 1 way.

The remaining ball must be blue, and there are 6 blue balls in the bag, so we can choose 1 blue ball out of 6 in C(6, 1) = 6 ways.

Therefore, the number of combinations of drawing three green balls is 1 * 6 = 6.

In total, the number of combinations of drawing with at least two green balls is 45 + 6 = 51.