Difference Between Permutation vs. Combination

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Main Difference

Permutation and Combination are Mathematical terms. Permutation is the arrangement of objects in which order is priority. Combination is the arrangement of objects in which order is irrelevant. Both are related to each other by formula P(n,r)=r!⋅C(n,r).

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What is Permutation?

Permutation is the arrangement of objects in which order is priority or important. It refers to an arrangement of a subset of a given size in combinations. It is the choice of r objects from a set of n objects without replacement and order of objects matters. Its formula is P(n,r)=n!/(nr)!. If you pick 1st, 2nd and 3rd place winners, it is permutation.

What is Combination?

Combination is the arrangement of objects in which order is irrelevant. It refers to number of subsets of a set of objects. It is the choice of r objects from a set of n objects without replacement and order of objects does not matter. Its formula is C(n,r)=n! / (nr)!r!. Picking the three winners is combination.

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Key Differences

  1. Permutation is the arrangement of objects in which order is priority or important while Combination is the arrangement of objects in which order is irrelevant.
  2. Formulae for Permutation is P(n,r)=n!/(nr)! while formula for combination is C(n,r)=n! / (nr)!r!
  3. In permutation order matters while in combination order does not matter.
  4. To pick up 3 people from a group of 10 then the combination will be 120. For picking a President, VP and a helper from a group of ten people then permutation is 720.
  5. Picking the two favorite colors from color brochure is permutation while picking any two colors from a color brochure is combination.
  6. If you pick 1st, 2nd and 3rd place winners, it is permutation and picking the three winners is combination.
  7. For arranging three objects “ABC”, the permutation will give its 6 arrangements while combination is only 1 arrangements.
  8. For picking two red candies from a box is permutation while picking any two candies from a box is combination.