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# Fundamental Principle of Counting : Multiplication Principle

**Fundamental Principle of Counting : Multiplication Principle**

**If an operation can be performed in any of n1 ways and if for each of these, a second operation can be performed in any of n2 ways , and if the first two operations have been performed, a third operation can be performed in any of n3 ways , and so on , then all these operations can be performed simultaneously in n1 * n2 * n3 ways.**

**Example One : Find the number of codes from the digits 4, 7, 8 (without repetition ).**

**Solution : 3 * 2 * 1 = 6 codes **

**That is the hundreds position can be chosen in three ways, the tens position in two ways and the units position in one way.**

**Example Two : Find the number of ways a voter can be classified if there are four income categories and five education categories,**

**Solution : 4 * 5 = 20 ways**

**Example Three: A furniture store has five warehouses and twelve retail outlets. In how many different ways can they ship an item from one of the warehouses to one of the stores?**

**Solution : 5 * 12 = 60 ways**

**Example Four : In how many ways can be a class of 35 students elect a president and a secretary assuming that no member can hold more than one position ?**

**Solution : 35 * 34 = 1, 190 ways**

**Example Five : In a doctorâ€™s office, there are ten issues of Time magazine, six issues of Readerâ€™s Digest and four issues of Asiaweeek . In how many ways can a patient waiting to see the doctor, glance at one of each type of magazine, if the order does not matter ?**

**Solution ; 10 * 6 * 4 = 240 ways**

**Example Six : How many number combinations are possible using three digits from 1 to 7 if repetition is allowed?**

**Solution : 7 * 7 * 7 = 343 ways.**

**Example Seven : In how many ways a 10-item True or False quiz be answered ?**

**Solution : 2^10 or 1024 ways**

**SOURCE : BASIC STATISTICS BY**

** Ang**

** Billiones**

** Dechavez**

** Diansuy**