We wish to select 6 persons from 8, but if the person A is chosen, then B must be chosen. In how many ways can selections be made?

A candidate is required to answer 7 questions out of 12 questions, which are divided into two groups, each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. Find the number of different ways of doing questions.

Out of 18 points in a plane, no three are in the same line except five points which are collinear. Find the number of lines that can be formed joining the point.

[Hint: Number of straight lines =¹⁸C₂ – ⁵C₂ + 1]

How many committee of five persons with a chairperson can be selected from 12 persons. [Hint: Chairman can be selected in 12 ways and remaining in ¹¹ C₄.]

How many automobile license plates can be made if each plate contains two different letters followed by three different digits?