Permutations
Permutation problems are similar to Combination problems with one major difference. Permutation problems take into account different
arrangements or ordering of the selected objects. In short, order counts in permutations. Suppose we wanted to select three people from seven without regard to order. We would select the combination formula and work the problem to find 35 ways to select three
people from seven people. Now, think of any one of the 35 possible choices of three people. One of the three could be named president, one could be named vice president and one could be named treasurer. Of the three selected people we have three choices for president, then two choices for vice president and finally only one choice for treasurer. Thus we can arrange our three selected people six different ways.
| One of the 35 combinations | The six permutations |
|---|
| ABC | ABC ACB BAC BCA CAB CBA |
So we must multiply the orginal 35 ways to select three people from seven by 6 for a total of 210 ways to select a slate of three officers.
The formula for computing permutations is
The slate of officers problem becomes:
Probability the most difficult counting problem for the student is determining whether order counts. If order counts, use the permutation formula. If order does not count, use the combination formula. One idea that may help is this. In your mind, draw the required number of objects, now ask, if I change the order of these objects or if I rearrange them will it matter? If you think order matters then select the permutation formula, otherwise select the combination formula.