Question

Three marbles are chosen from an urn that contains 6 red, 4 white, and 5 blue marbles. How many samples containing at least 2 blue marbles are possible?

Answer 1

The number of samples containing at least 2 blue marbles is 110.

Step-by-step explanation:

To find the number of samples containing at least 2 blue marbles, we need to consider the different combinations of choosing marbles from the urn. In this case, we can have:

• 2 blue marbles and 1 marble that is not blue
• 3 blue marbles

First, let's consider the case of 2 blue marbles and 1 marble that is not blue. We can choose 2 blue marbles from the 5 blue marbles in the urn in C(5, 2) = 10 ways. For the marble that is not blue, we can choose it from the remaining marbles in the urn, which include the 6 red marbles and 4 white marbles. So, we can choose this marble in C(10, 1) = 10 ways. Therefore, the number of samples with 2 blue marbles and 1 marble that is not blue is 10 * 10 = 100.

Now, let's consider the case of 3 blue marbles. We can choose 3 blue marbles from the 5 blue marbles in the urn in C(5, 3) = 10 ways. Therefore, the number of samples with 3 blue marbles is 10.

Adding up the two cases, the total number of samples containing at least 2 blue marbles is 100 + 10 = 110.