# Difference Between Permutation and Combination

A permutation is for lists where does order matters but in Combination, it doesn’t. Practically, both involve selecting a subset from several elements.

With a simple example, when you return from the market, if your mom asks about the price, you should say it 235 (which is actual), not 325 or 532. That’s Permutation.

## Permutation vs Combination

The main difference between Permutation and Combination is that in a permutation, the order of the elements is taken into consideration and a permutation can be either with repetition or without repetition. In a combination, the order of the elements is not a matter of concern.

## What is Permutation?

‘Permutation’ is defined as an arrangement that can be done using some of the objects or items in an ordered manner. It’s all about arrangement.

Suppose, a smartphone is locked by a PIN code which is 9396. To unlock, it won’t open if you enter 9693, because there is a different ordering for your smartphone’s PIN.

## What is Combination?

‘Combination’ is defined as the selection that can be done using some of the items where order does not matter.

## Main Differences Between Permutation and Combination

The difference Between Permutation and Combination are clearly explained below:

1. Placement and order is the main difference between permutation and combination. In permutation, we are restricted to comply with an order but in combination, there is no such restriction.
2.  A permutation is just an arrangement of the things where the arrangement will be in a specific order. The combination is a selection where the selection is without any specific order.
3. In Permutation, the number of arrangements is denoted by nPr.
4. Multiple permutations can be derived from a single combination but only a single combination may be derived from one permutation.
5. A permutation is the choice of ‘r’ things from the group or set of ‘n’ things with the order. The combination is a selection of ‘r’ things from the large set or group of ‘n’ things without any specific order.

## Conclusion

After knowing the above differences thoroughly, it was understood that Permutation and Combination are completely different terms which are the so-called ways with the field of Mathematics. In these two different terms, we are always concerned about arrangement and selection.

## References

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