word problem

[hakyology]

a scientist used a unique two-color coe to identify each of the rest subjects involved in a certain study. if the sicnetist found that choosing from among six colors produced enough color codes to identify all but 5 of the rest subjects, how many test subjects were in the study? ( assume that the order of the colors in the codes does not matter.)
A) 7
B) 10
C) 15
D) 17
E) 20

Plesase explain. I do not know the answer though.

[dbart06]

I will take a shot:

given 6 differnet colors, choosing combinations of 2:

6c2 which is 6!/2!(6!-2!) = 15

we also know that the total combination is 5<total subjects

Thus the anwer is 20 total subjects.

What is OA?

[dbart06]

I will take a shot:

given 6 differnet colors, choosing combinations of 2:

6c2 which is 6!/2!(6!-2!) = 15

we also know that the total combination is 5<total subjects

Thus the anwer is 20 total subjects.

What is OA?

[olika]

I got 20, too.
But the logic is different.
If we need two colors to code 5 subjects and 6 colors to code the rest (x-5, where x= number of all subjects), then (x-5)*2/30. Finally, we get x-5=15, then x=20.