# Fundamental Principles of Counting

There are two fundamental principles - principle of addition and principle of multiplication. These two principles enable to understand permutations and combinations and form the base for permutations and combinations.

### Fundamental Principle of Multiplication

If there are two jobs such that one of them can be completed in m ways, and when it has been completed in any one of these m ways, second job can be completed in n ways; then the two jobs in succession can be completed in m × n ways.

**Explanation**

If the first job is performed in any one of the m ways, you can associate with this any one of the n ways of performing the second job and thus there are n ways of performing the two jobs without considering more than one way of performing the first. So corresponding to each of the m ways of performing the first job, you have n ways of performing the second job.

Hence, the number of ways in which the two jobs can be performed is m × n.

### Fundamental Principle of Addition

If there are two jobs such that they can be performed independently in m and n ways respectively, then either of the two jobs can be performed in (m + n) ways.