Permutation and Combination

The concepts about permutation and combination form an important part of mathematics and quantitative aptitude. Both permutations, as well as combinations, are simply two unique ways of representing a number of elements. Briefly, we may describe permutation as the way of representing elements such that the order of elements is crucial. One may also say that permutation is an ordered combination. On the other hand, in a combination is the way of selecting elements from a set in such a way that the selection order does not play an important role.

There are mainly two types of permutations:

• Repetition is allowed – For example, the lock of a suitcase can be 5,5,5
• Repetition is not allowed – For example, in a competition, an individual can either secure first, second or third place but not two places at once

There are mainly two different types of combination:

• Repetition is allowed – For example, the note in your hand, 10, 10, 20, 100, 100
• Repetition is not allowed – For example, lottery numbers, 7, 19, 20, 67, 89

The formula for permutations with and without repetition

Various different formulas are used for resolving problems concerning permutations and combinations.

1. Permutation formula when repetition is allowed:

NPR = NR Where, P = Permutation, N = No. of things to choose from, R = No. of things chosen.   2. Permutation formula when repetition is not allowed: NPR = N! / (N-R)! Where, N = No. of things one can select from, R = No. of things actually selected.

The formula for combination for with as well as without repetition

1. Combination formula when repetition is allowed:

NCR = (N + R – 1)! / [R! (N – 1)!] Where, N = No. of things to select from , R = No. of things selected, C = Combination of distinct things.  2.Combination formula when repetition is not allowed NCR = NPR / R! = N! / (N-R)! R! Where, C = Combination, N = Different things, R = Different things taken R at a time. These are the various formulas for both combination and permutation.

Difference between combination and permutation

While both combination and permutation form a crucial part of Mathematics and quantitative aptitude, both these concepts differ from one another. A few of these differences are listed below:

• From the above discussion, it can be easily inferred that one primary difference between permutation and combination is that in permutation the selection order plays an important role whereas in combination selection order is not considered
• Based on the first point itself, it can be said that the permutation is used for lists wherein the order is important whereas combination is used for groups wherein order does not matter
• A permutation can help in understanding the arrangement regarding items whereas a combination cannot do so
• Multiple permutations might be taken out from one combination whereas only one combination might be taken out from one permutation
• Permutation can also be referred as ‘ordered elements’ on the contrary combination can also be referred as ‘unordered sets’

Thus, the above-listed points help in differentiating between permutation and combination.

Conclusion

It can be concluded that the concept of permutation and combination forms a crucial part of mathematics and quantitative aptitude. Permutation can be explained as the way of representing elements such that the order of elements is crucial. It is of two types when repetition of elements is allowed and another when repetition of elements is not allowed. Depending on the requirements the specific formula for each can be chosen. The combination can be explained as the way of selecting elements from a set in such a way that the selection order the does not play an important role. Again, the combination can also be of two types, when repetition of elements is allowed and another when repetition of elements is not allowed. Depending on the requirements the specific formula for each can be chosen. The primary difference between a permutation and a combination is that in a permutation the order of elements is crucial whereas in a combination the order of elements is not crucial.