Solving math permutation Problems is quite an easy task. But solving math Permutation Problems without Permutation Calculation or without Permutation Formula is an easier as well as interesting task. Solving without Permutation Calculation means that we solve math Permutation Problem without using Permutation Formula. Remember, each math Permutation Problem asks you to arrange *n* number of items in a group of *r* items, where order matters. Here arises the concept of Sets which is the key to solving math permutation Problems without Permutation Calculation or Permutation Formula. Number of items which you are going to be arranged constitutes Basic Set while group of items into which this Basic Set has to be arranged is Sub Set. All what you have to do is to identify Basic Set and Sub Set. After you have identified these two sets in math Permutation Problems, see whether order of arrangement matters. If it matters it means that it is a math problem of Permutation.

Now you are ready for solving math permutation problems without Permutation Calculation or Permutation Formula.

Consider following example which solves Permutation Problem without involving Permutation calculation or Permutation Formula.

Example1

There are three doors to a science lab. In how many ways a scientist can enter the lab from one door and leave from the other door?

Solution

Keep in mind that we’ve to solve this Permutation Problem without Permutation Calculation. Now suppose A, B, C are three doors to the science lab. So [A, B, C] is Basic Set. Here order matters as we cannot consider entry from door A and exit from door B same as entry from door B and exit from door A. We are to arrange two doors (one for entry and one for exit), this constitute Sub Set. Now without any Permutation Calculation we see that following arrangements (sub sets ) of 2 doors out of Basic Set of 3 doors [A, B, C] are possible:

[A, B] [A, C] [A, D] [B, C] [B, D] [C, D]

Without involving any Permutation Calculation or Permutation Formula, the answer is 6.

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Before I read this web page, I used to think it quite impossibe to solve permutation problems without involving calculations. Great stuff!