Probability question

rsvaishu wrote:A "complete set" of disk consist of one green disk, one blue disk, one orange disk and one purple disk. A bag contains 12 green disks, 12 blue disks, 12 orange disks and 12 purple disks The bag contains nothing else. If 6 disks are randomly selected from the bag, what is the greatest possible number of complete set of disks that could be remaining in the bag?

A. 5
B. 6
C. 8
D. 9
E. 10

The greatest possible number of complete sets will occur when someone would take 1 green, 1 blue, 1 orange, and 1 purple disk. In other words, one disk of each color and then take another 2 disks of different colors, for instance 1 green, 1 blue.
This will reduce the number of green and blue disks to 10 of each color. While orange and purple will be 11 of each color. The number of disks of these two colors - green and blue - will limit the greatest possible number of complete sets of four different disks to 10.

1. Imagine we have 4 piles with disks of different colors;

12Green 12Blue

12Orange 12Purple

2. First, take 4 disks from the bag. To maximize the number of complete sets take 4 disks of different colors. We get:

11Green 11Blue

11Orange 11Purple

3. Second, take another 2 disks from the bag. Again, to maximize the number of complete sets take 2 disks of different colors. We get:

10Green 10Blue

11Orange 11Purple

We have 10 complete sets of disks.
Another way to take these disks is to grab 3 pairs of different colors. The answer will be the same though.
The answer is E.

12*4=48
6 discs removed...so left with 42 discs
to make complete set we have to 42\4= 10 and remainder as 2

so max set can be 10
so E.