Permutations vs. Combinations

Difference Between Permutations and Combinations

Combination and Permutation appear the concept related to the ‘arrangement of objects’. They are similar origin and are related to each other. The difference is that both of them are used in different situations. The combination does not focus on patterns or orders. An example below clearly explains this.

In a tournament many teams participate. It does not matter how team ‘x’ and team ‘y’ are listed. Both the teams are similar.  If the team ‘y’ plays with team ‘y’ or vice versa, it will not matter. What matters is that both should have equal chance to play with each other. The order does not matter. Making a team of ‘k’ number of players out of ‘n’ number of players available is an example of combination.

The equation for computing ‘combination’ problem is as follow.

nk (or n_k ) = n!/k!(n-k)

‘Permutation’ on the other hand is concerned with standing tall in an ‘Order’. The pattern of objects is important in permutation. When sequence is important, the permutation is necessary. Permutation has higher numerical values as compared to the combination. The example of permutation is to form a four digit number using 1,2,3,4,5.

For example five students want to take a group photos. In one photo the stand in ascending order as 1, 2, 3, 4, 5. In second photo they change the order thus: 1, 2, 3, 5, 4. The second order is entirely different from the first one. Permutation can be expressed through the following equation:

nk (or n^k) = n!/(n-k)

There is difference between combination and permutation. The basic difference is that Permutation gives higher values in its result as exemplified by the following equation:

n^k = k! (n_k)

Combination problem are unique in nature.


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