SQUINGEL wrote:
Is there any other way to solve this question?
Well 'counting' is the only method applicable for this question.
As you are being asked to find the 'minimum' value, use the options to guide you.
Options A and B are out because of obvious reasons.
Start with E, Lets say you have 5 colors. Out of these 5 colors, look at how many 2 color combinations you can create = 5C2 = 10 and remaining 2 can be single colors. So there you go, you have your answer. An answer that will give you possible number of combinations \(\geq\) 12 will be the answer as you need to cover all 12 clients
uniquely.
If lets say the total number of clients would have been = 23, then with n = 5, you could at most have = 5C2 + 5 = 15 (<23) different ways, with n =6 you could have 6C2 + 6 = 21 different ways (<23). Thus n = 7 would have been the minimum number of colors.
Hope this helps.