Permutations and Combinations -- How Can They

Permutations and combinations -- How can they be used in business today? Certain types of probability outcomes involve dividing the numbers of potential outcomes into sets, and dividing them along the lines of possible, projected outcomes. For simple problems of division, the individual considering the problem can count the outcomes. But, to consider a spread of larger numbers of potential outcomes, as would be likely in a business setting; one must use the statistical methodology of permutations and combinations.

Combinations count the number of ways of choosing a certain number of distinct or specific objects, without regards to order -- only the number of ways of choosing them is considered. Permutations involve pairing up certain objects with other objects and counting the potential combinations or outcomes that result from generating different combinations within specified limits.

Because the 'real world' and life of business often has such limits, from staffing schedules to products that must be used and paired with other products, the use of permutations and combinations is extremely important. According to "Dr. Math," the easiest way to explain "permutations" in combination on a theoretical level is to suppose an individual wants to find the number of ways to arrange the three letters in the word CAT in different two-letter groups.

One sets a variety of permutations upon this problem, for instance, "where CA is different from AC and there are no repeated letters. Because order matters, we're finding the number of permutations of size 2 that can be taken from a set of size 3. This is often written 3_P_2. We can list them as: CA CT AC TC TA." (Dr. Math, 2004) All well and good, but how could this be useful to a business owner? Interestingly enough, and concerns about super-sizing and fat and calories aside, Dr.

Math also uses the example of McDonald's meals as a way of giving real life examples of permutations and combinations. For instance, when McDonald's introduced a special menu with 8 different items, an advertisement for the fast food chain claimed that this created 40312 possible combinations. In fact, Dr. Math calculated that "his total is going to be a lot bigger than 40312," and that was assuming, in his set up, far fewer items than actually allotted upon the menu. (Dr.

Math, 2004) Beyond speculating about advertising, however, the use of permutations and combinations can be useful, for instance, when a business desires to allocate its advertising for several products along several potential sources, all from the same media such as television or magazines, but wishes to make sure that the combinations of the different publications did not overlap in terms of the combinations.

To calculate, the various letters could be used to represent the publications, and the products also allocated various letters, to ensure that there was no overlap of particular products and sources.

Restaurant owners could use permutations and combinations to determine various pairings of toppings, to determine if this was economically feasible to achieve -- for instance, what is the maximum amount of combinations a pizza can have, given a fixed array of toppings, and also, what is the maximum amount of toppings that any singular pie can possess? Thus, the owner could calculate the maximum amount of funds the pizza could possibly allocate to the owner of the pizza business.

Permutations in combination could also be used to pair off different members of staff, when needed, on the.