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.]

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]

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?

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

A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected from the lot.