Counting Techniques

Fundamental Principle of Counting

If there are $m$ ways to do a task and $n$ ways to do another task, the number of ways to do the first then the second task is $m \times n$.
 

In this video

1. How many 5-digit numbers can be made out from the digits 4, 6, 7, 8 and 9?
2. In how many ways can 5 students be seated on a bench?
3. Three-digit numbers are to be made out from the digits 0, 1, 2, 3, 4, 5, 6, and 7. Repetition of digit is not allowed.
   
   1. How many such numbers can be made?
   2. From 3-a, how many are greater than 400?
   3. From 3-a, how many are even numbers?
   4. From 3-a, how many are odd numbers greater than 300?
4. How many ways are there to label the four corners of a square with letters from English alphabet such that...
   
   1. each corner gets a different letter?
   2. adjacent corners get different letters?
5. In how many ways can 6 individuals be seated in a round table with 6 chairs?
   
   1. Suppose 2 persons wanted to be seated side by side, in how many ways can they do it?
   2. In how many ways can these 6 individuals arrange themselves if 2 among them refuse to sit together?