A bag contains a collection of distinguishable marbles. The bag has three red marbles, five green ones, one lavender one, two yellows, and six orange marbles. How many sets of four marbles include exactly two green marbles? (Note that this means there must be two other non-green marbles as well).

The total number of sets is 2,640.

Step-by-step explanation:

The number of marbles in the bag are:

S = {3R, 5G, 1L, 2Y and 6O}

There are a total of N = 17 marbles in the bag.

Four marbles are randomly selected.

Assume that the selection was without replacement.

It is provided that two of the marbles are green.

And the remaining two are non-green.

A sample of the selection is as follows:

G, G, _, _

The two green marbles can be selected in 5 × 4 = 20 ways.

So, the remaining two marbles cannot be green.

That leaves us with: 3R, 1L, 2Y and 6O = 12 marbles.

The third marble can be selected in 12 ways.

And the fourth marble can be selected in 11 ways.

So the number of combinations of selecting 4 marbles such that 2 are green and 2 are non-green is:

Total number of sets = 5 × 4 × 12 × 11 = 2640

Thus, the total number of sets is 2,640.

answer: 7270

step-by-step explanation: