Discrete Maths, Lecture-11 : Counting-I

These are my notes from 11th lecture of discrete mathematics course taught at Arsdigita university by Shai Simonson. Other posts relating to this are here.

In Summary, this lecture covers following things...

• 5 important principles of counting(2 official and 3 unofficial ones) namely Multiplication principle, Addition principle, Counting the Opposite, Counting double and Just another principle.
• Permutation and Combination(and its relation to Binomial coefficients)
• Interesting observations of Pascal's triangle
• Ways to prove theorems using counting arguments.

A general thing that always helped is that when you're solving some general case n, observe the behaviour for small values of n such as 1,2,3 etc .. this gives good insight/understanding into the problem.

Here are my notes....
Note: Unless specified otherwise, in these notes n objects implicitly mean n distinct objects.