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Discrete Mathematics by Babu Ram

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2

Counting

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

2.1 ADDITION RULE

If a set A is the union of n distinct mutually disjoint subsets A1, A2, …, An, then

 

|A| = |A1| + |A2| + … + |An|,

where |Ai| denotes the number of elements in the set Ai.

The addition rule can also be stated as

If an event E1 can occur in m ways and an event E2 can occur in n ways, then E1 or E2 can occur in m + n ways.

EXAMPLE 2.1

Let E1 be the event of choosing an odd number between 10 and 20 and E2 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}, E1 can occur in five ways. Similarly even numbers ...

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