What is the difference between permutation and combination?

The key difference is order. In permutations, the order of selection matters (e.g., arranging letters in a word). In combinations, the order does not matter (e.g., picking a team of players from a group).

Why is the number of permutations always greater than or equal to combinations?

For any set of 'n' and 'r', permutations consider every different arrangement of the 'r' items as a unique outcome. Combinations, however, count all these different arrangements as a single outcome. Since permutations count more possibilities, the number is always larger, unless r=0 or r=1, where they are equal.

Permutation & Combination

Calculate permutations (nPr) and combinations (nCr) effortlessly.

Permutation (nPr)

Total Items (n)

Items to Choose (r)

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About Permutations & Combinations

What is the Difference?

Permutations and combinations are two fundamental concepts in combinatorics that deal with counting the number of ways to select or arrange items from a set. The key difference between them is whether the order of selection matters.

Permutation (nPr): An arrangement of items where order matters. For example, if you are choosing the 1st, 2nd, and 3rd place winners in a race, the order in which they are chosen is important. "ABC" is a different outcome from "BCA".
Combination (nCr): A selection of items where order does not matter. For example, if you are choosing a committee of 3 people from a group of 10, the order in which you pick them doesn't change the final committee. "ABC" is the same as "BCA".

How to Use This Calculator

Select the appropriate tab, either "Permutation (nPr)" or "Combination (nCr)". In both cases, you need to provide:

Total Items (n): The total number of items in the set you are choosing from.
Items to Choose (r): The number of items you are selecting or arranging.

Click "Calculate" to get the result. Note that for any given 'n' and 'r', the number of permutations will always be greater than or equal to the number of combinations.

Practical Applications

These concepts are crucial in many fields, including statistics, computer science, and engineering.

Password Security: Calculating how many possible passwords can be formed from a set of characters.
Lotteries and Games: Determining the odds of winning a lottery or drawing a specific hand in a card game.
Quality Control: Figuring out how many ways a sample can be selected from a batch for testing.
Scheduling: Calculating the number of different ways tasks or people can be scheduled.