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| Fundamental Principle of Counting |
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| Suppose two events E1 and E2 are to be performed in sequence, then if E1 can be performed in 'm' ways and for each of these ways E2 can be performed in 'n' ways, then the sequence E1E2 can be performed in 'mn' different ways. This is known as the Fundamental Principle of Counting. |
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| Multiplication Principle: |
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| The same principle can be generalized to three or more events occurring in succession as follows: |
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| If n operations can be performed in m1,m2,m3,...mn ways respectively, then all n operations in succession can be performed exactly in m1,m2,m3,...mn ways. |
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| The above principle is called multiplication principle. |
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| Addition Principle: |
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| If two events E1 and E2 can occur independently in exactly m ways and n ways respectively, then either of the two events can occur in (m + n) ways. |
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| Example 1: |
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| There are 8 cars plying between two towns A and B. In how many ways can a person go from one town to the other and return by a different
car? |
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| Suggested answer: |
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| There are 8 ways of travelling from A to B and seven ways for the return journey, since he cannot come by the same
car. Hence, the number of ways of making both the journeys is 8 x 7 = 56. |
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| Example 2: |
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| How many numbers are there between 100 and 1000 such that every digit is either 2 or 9? |
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| Suggested answer: |
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| Number of ways of filling hundred's place = 2 |
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| Number of ways of filling ten's place = 2 |
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| Number of ways of filling unit's place = 2 |
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| By the fundamental principle of counting, the total number of numbers = 2 x 2 x 2 = 8. |
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