What is the difference between permutation and combination?

Step-by-step explanation: A permutation is an arrangement of certain objects in which order matters.

Let's look at an example.

Find the number of permutations for the letters A, B, and C.

In this example, we want to find the number of permutations of the letters A, B, and C.

Let's start by listing the permutations. Let's start with the permutations that begin with the letter A.

Permutations for A - ABC   ACB

Next, let's list the permutations that begin with B.

Permutations for B - BAC   BCA

Finally, let's list the permutations that begin with C.

Permutations for C - CAB   CBA

If we count the number of permutations, we can see that there are 6 permutations for the letters A, B, and C.

On the other hand, combinations are arrangements in which order does not matter.

For example, AB is the same as BA. Let's look at an example.

List the combinations you can have by choosing 2 of the letters below.

A, B, C, D

It's important to understand that we don't need to list arrangements with the same letters in a different order because with combination, order is not important.

Let's begin by listing the combinations that begin with A.

Combinations for A - AB  AC  AD

Now, let's list the combinations that begin with B.

Combinations for B - BC  BD

Notice that I didn't list BA because BA is the same as AB so we don't need to list it again since we're dealing with combinations.

Now, let's list the combinations that begin with C.

Combinations for C - CD

Notice that I didn't list CA or CB because CA is the same as AC and CB is the same as BC. Remember, order is not important.

All of the combinations that begin with D have already been listed. So the combinations with 2 letters from the letters A, B, C, and D are AB, AC, AD, BC, BD, CD.

To summarize, permutations can be an arrangement of letters, objects, numbers and so on. Combination are also arrangements but order does not matter.

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