Question

A "complete set" of disks consists 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 sets of disks that could be remaining in the bag?

Answer 1

The greatest number of complete sets that could be left is 10

Explanation:

Firstly, we should know that since there are 12 sets of each type of disks, the number of complete sets that we have is 12 sets.

Now, we intend removing 6 disks. The kind of removal that could leave the greatest number of sets is one such that each of the disks have one of its members removed, now that will make a total of 4. we still have two left. That means we can then randomly select any other two.

The picture i’m trying to paint is that for example , if one green, one blue , one purple and one orange disks are removed, this means we have removed entirely a set of disks. Wherein we still have 2 disks to remove. we can still try to remove the renaming two disks from another single set making it affected.

The total number of sets thus affected would be 2. If we subtract this from the total number of sets which is 12, we have 12-2 = 10 complete sets left