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Fundamental Principle of Counting : Multiplication Principle

Updated on November 16, 2011

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 doctor’s office, there are ten issues of Time magazine, six issues of Reader’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







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      Maria Cristina Aquino Santander 6 years ago from Manila

      Hi carcro great to see you on this Math hub. Thank you for taking time to visit this hub. Your visit and comments are much appreciated. Remain blessed and best regards.

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      Paul Cronin 6 years ago from Winnipeg

      I have always loved math. I guess I must be a nerd but its always come easy to me. Thanks for sharing your math tips with the masses!