Aptitude Discussion

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. |
$8$ |

**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**.

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