Consider a bag of jelly beans that has 30 red, 30 blue, and 30 green jelly beans. a) How many color combinations of 15 beans have at least 6 green beans

Using the combination formula, it is found that there are 17,157,323,000,000,000 color combinations of 15 beans have at least 6 green beans.

The order in which the beans are chosen is not important, hence, the combination formula is used to solve this question.

Combination formula:

is the number of different combinations of x objects from a set of n elements, given by:

Th total number of combinations of 15 beans from a set of 30 + 30 + 30 = 90 is:

With less than 6 green, we have:

0 green:

1 green:

2 green:

3 green:

4 green:

5 green:

Hence, the total for the number of combinations with less than 5 green is:

Subtracting the total amount of combinations from the number with less than 5 green, the number of combinations with at least 6 green is:

There are 17,157,323,000,000,000 color combinations of 15 beans have at least 6 green beans.

A similar problem is given at link

680

Step-by-step explanation:

Number of red beans = 30

Number of Blue beans = 30

Number of green beans = 30

How many color combinations of 15 beans have at least 6 green beans?

Since at least 6 of the beans must be green,

Then (15 - 6) = 9

Then, the remaining 9 could be either red, blue or green.

Therefore, C(9 + (9 - 1), 3)

C(17, 3) = 17C3

nCr = n! ÷ (n-r)! r!

17C3 = 17! ÷ (17 - 3)! 3!

17C3 = 17! ÷ 14!3!

17C3 = (17 * 16 * 15) / (3 * 2)

17C3 = 4080 / 6

17C3 = 680 ways

astronomers is your final answer! : )

4x and 6y

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