Permutation-Combination
Aptitude

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Q.

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.

$8$

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Solution:
Option(B) is correct

Each one coded with either a single colour or unique two-colour pair.

Therefore, total number of ways $= n + {^nC_2}$

Minimum number of different colour needed to code all 20 chemicals will be 6.

$= 6 +{^6C_2} = 21$


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