7C2 = 21, then** how can we color 26 letters distinctively using 21 color combinations**. If we consider that pair (Red, Green) and (Green, Red) as two different pair then we will get 42 combinations. However , by this logic we get 6C2 = 15 that means 30 color combinations. **Since, in question it is asked minimum value of k, then the answer should be 6(Option D).**

Now if consider that color pair (Red, Green) = (Green , Red ) then 8C2 = 28 , **then by this logic answer should be 8(Option B).**

**In either case, 7(option C) can't be the correct answer**. Am I missing anything here? Please explain.

Thank you.