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Statistics of permutations and combinations












































In mathematics, both Permutations and Combinations refer to how many different ways the elements within a set can be arranged.

The following problem illustrates how these two concepts can be applied to determine the number of unique breakfast menus which can be created from the food choices available:


You wake up in the morning and go to the kitchen to look for breakfast.

You have a choice of brownies, muffins, cheesecake, or cereal.

To drink you have a choice of fresh milk, hot chocolate, iced tea, orange juice, apple juice, or water.

Your mother also insists that you take a multi-vitamin with your breakfast. You can choose from Flintstones vitamins, Enervon vitamins, or Centrum vitamins.


How many possible breakfast menus can be made up if you combine one entrée, one drink, and one brand of vitamins?

Comments for Statistics of permutations and combinations

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Jan 05, 2014
every possible breakfast menu
by: Staff


Answer

Part I


When the order (the sequential arrangement of the menu choices) is important, all of the possible arrangements are called Permutations.

If the order in which you choose the entrée, drink, and brand of vitamins is important, then the following is true:

The arrangement of the three choices {entrée, drink, brand of vitamins} is not the same menu as those same three choices in a different order {entrée, brand of vitamins, drink}.

As you can see, calculating permutations for this particular problem does not make any practical sense.

(However, calculating permutations is important for certain types of problems.

For example, customer PIN numbers use the same digits over and over.

Order is important.

The PIN {1,2,3,4} is not the same as the PIN {4,3,2,1}, even though the same digits appear in both.

If a bank wanted to know how many unique, four-digit PIN numbers are available to their customers, calculating permutations makes perfect sense.)


When the order (the sequential arrangement of the menu choices) is not important, all of the possible arrangements are called Combinations.

A Combination means that the arrangement of the same menu choices can be in any order.

{entrée, drink, brand of vitamins} is the same as the menu as {entrée, brand of vitamins, drink} or {drink, brand of vitamins, entrée }, and so on.

These three menus are counted as one combination. All three menus use exactly the same selections, regardless of the order.




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Jan 05, 2014
every possible breakfast menu
by: Staff


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Part II


When the order (the sequential arrangement of the menu choices) is not important, all of the possible arrangements are called Combinations.





These three menus are counted as one combination.  All three menus use exactly the same selections, regardless of the order.








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Jan 05, 2014
every possible breakfast menu
by: Staff


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Part III


possible entrée choices: 4 {brownies, muffins, cheesecake, cereal}

possible drink choices: 6 {fresh milk, hot chocolate, iced tea, orange juice, apple juice, water}

possible multi-vitamin choices: 3 {Flintstones vitamins, Enervon vitamins, Centrum vitamins}



possible entrée choices: 

       4 {brownies, muffins, cheesecake, cereal}

possible drink choices: 

       6 {fresh milk, hot chocolate, iced tea, orange juice, apple juice, water}

possible multi-vitamin choices: 

       3 {Flintstones vitamins, Enervon vitamins, Centrum vitamins}








-------------------------------------------

Jan 05, 2014
every possible breakfast menu
by: Staff


-------------------------------------------


Part IV


the number of menu combinations is: 4 * 6 * 3 = 72 different menus possible



number of possible menu choices (combinations)





72 possible menu choices (combinations)








Thanks for writing.

Staff
www.solving-math-problems.com


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