In a certain laboratory, chemicals are identified by a colour-coding system. There are 20 different chemicals. Each one is coded with either a single colour or a unique two-colour pair. If the order of colours in the pairs does not matter, what is the minimum number of different colours needed to code all 20 chemicals with either a single colour or a unique pair of colours?

A. 7

B. 6

C. 5

D. 8

Answer: Option B

Solution(By Examveda Team)

Each one coded with either a single colour or unique two-colour pair.
Therefore, total number of ways = n + ⁿC₂
Minimum number of different colour needed to code all 20 chemicals will be 6
= 6 + ⁶C₂
=21