In our everyday life, we come across many different counting problems. There are two basic counting principles—Addition Rule and Multiplication Rule.

If a set *A* is the union of *n* distinct mutually disjoint subsets *A*_{1}, *A*_{2}, …, *A*_{n}, then

|*A*| = |*A*_{1}| + |*A*_{2}| + … + |*A*_{n}|,

where |*A*_{i}| denotes the number of elements in the set *A _{i}*.

The addition rule can also be stated as

If an event E_{1} can occur in *m* ways and an event E_{2} can occur in *n* ways, then E_{1} or E_{2} can occur in *m* + *n* ways.

**EXAMPLE 2.1**

Let E_{1} be the event of choosing an odd number between 10 and 20 and E_{2} be the event of choosing an even number between 10 and 20. Since odd numbers between 10 and 20 are {11, 13, 15, 17, 19}, E_{1} can occur in five ways. Similarly even numbers ...

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