How to solve a Permutation Problem easily?

In order to understand as to how to solve a Permutation Problem easily, you must have a clear-cut concept of what is a Permutation?

Permutation is basically arrangement of some objects or values into a particular way where order is important. Now the question is what is the meaning of “where order is important”? The whole secret of how to solve a Permutation Problem easily lies in understanding of this phrase. In math word problems that ask you to arrange some objects or values in a way that order is important, it means that you are being asked to solve a Permutation problem. Some times, a Permutation Problem does not tell you that order is important. In such a Permutation Problem you’ll have to recognize on your own whether the order is important. Recognizing the importance of order correctly gives you the answer of how to solve a Permutation Problem easily. On this basis you’ll see following two types of Permutation Problems.

1. A Permutation Problem where importance of order is given
2. A Permutation Problem where importance of order is NOT given

Now we illustrate above two types of a Permutation Problem with examples so that you can find answer of how to solve a Permutation Problem easily.

1. A Permutation Problem where importance of order is given

In a permutation problem where it is said that order is important it means that AB ≠ BA. Although arrangements, AB and BA, seem to be alike, a Permutation Problem counts both the arrangements as two.

Example

Arrange four letters ABCD in group of two where order is important.

Solution

Since in question it is given that the order is important, it means you’ll have to solve a Permutation Problem. Possible arrangements are as follows:

• AB, AC, AD
• BA, BC, BD
• CA, CB, CD
• DA, DB, DC

You can see that following groups are same

I.            AB and BA
II.          AC and CA
III.        AD and DA
IV.         BC and CB
V.           BD and DB
VI.         CD and DC

Since above six groups of two pairs are same, we should count half of them and answer should be 6. But in question it is given that order is important, so we cannot ignore any order and we will count 12 arrangements. Therefore, answer will be 12.

Now we illustrate type 2 of a Permutation Problem to find the answer of how to solve a Permutation Problem easily?

2. A Permutation Problem where importance of order is NOT given

In math word problem that asks you to arrange some objects or values in a particular way and it is not mentioned that “order is important” it means that importance of order is hidden. First recognize the importance of order, then solve question as a Permutation Problem, if order is important.

Example

You have to select a subcommittee of 2 members out of a committee of 3 members. How many arrangements are possible?

Solution

Suppose A, B, C are three members of the committee.  Then 12 arrangements are possible as explained above, if order is important. But in committee repetition of people is not possible. It means that here order is NOT important. So we cannot solve this question as a Permutation Problem.

In such questions where order is NOT important (AB=BA) we usually use concept of math Combination instead of math Permutation. For detail read How to solve Combination Problems easily?

By making practice of recognizing importance of order you can answer the question how to solve a Permutation Problem easily?