If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### Course: Integrated math 2>Unit 13

Lesson 2: Counting with combinations

# Intro to combinations

Learn the difference between permutations and combinations, using the example of seating six people in three chairs. Permutations count the different arrangements of people in specific chairs, while combinations count the different groups of people, regardless of order or chair.

## Want to join the conversation?

• it says combinatations do not matter
however suppose there is a locker combination, the order matters so why is a combianation nmattering
• You're talking about a permutation, even though in the real world people use the word combination (which is mathematically wrong).

Here's an easy way to remember:
- If a group consisting of Alice, Bob and Charlie has the same meaning as a group consisting of Charlie, Alice and Bob, you're talking about a combination.

- If a group consisting of Alice, then Bob and THEN Charlie is NOT the same meaning as a group consisting of Charlie, then Alice and THEN Bob, you're talking about a permutation.

• Are permutations and combinations the same thing? I thought that in combinations you couldn't use the same people. Like in combinations we could do :CBA but we couldn't do BCA because they are the same people. And in permutations we could do :CBA and BCA because order didn't matter. I'm soooo confused!
• In Permutations the order matters. So ABC would be one permutation and ACB would be another, for example. In Combinations ABC is the same as ACB because you are combining the same letters (or people). Now, there are 6 (3 factorial) permutations of ABC. Therefore, to calculate the number of combinations of 3 people (or letters) from a set of six, you need to divide 6! by 3!. I think its best to write out the combinations and permutations like Sal does; that really helps me out.
• I don't understand, at Salman says, to find the number of ways to arrange three people from the six, the equation is 120 (total number of permutations) divided by 6 (number of ways to arrange the letters in a set). Why wouldn't the equation to find all arrangements of three people be the same as finding the total number of possibilities in a set? (3 letters*3chairs = 9 different arrangements)
• There are 3 people who can sit in chair one. Then there are only two of those three left for chair two and then one for chair three. 3*2*1 equals 6
• Just being curious, is the word 'permutation' in any way related to mutation
(per-mutation)?
• Yes it is. A "mutation" is a change, and the prefix per- means something like "very" or "thorough". So a permutation can be interpreted as a "thorough change".
• In How many ways can 5 letters be posted in 4 postboxes if each postboxes can contain any number of letters ?

• Each of the 5 letters has 4 possibilities for where it can be, so the number of results is 4*4*4*4*4 or 4⁵
• How to remember the difference between combination and permutations?
• combinations:(C)arefree of the order.
permutations: needs order, very (P)ragmatic.
P is a pragmatic parent. C is a carefree child.
Saw that in some website months ago.....

• neden altıya bölüyoruz 3 kişiyse 3 e bölmemiz gerekmez mi ?
• i do not understand that language
• What is the formula for combination and permutation? This one did not make sense
• Formula for permutation:
nPr = n!/(n-r)!
Formula for combination:
nCr = n!/r!.(n-r)!

Difference between permutation and combination
​*In permutations, the order matters*, so rearranging the order of selected objects results in different permutations. *In combinations, the order does not matter*, so different arrangements of the same set of objects are considered equivalent.

Permutations: AB and BA are considered different permutations because order matters.
Combinations: AB and BA are considered the same combination because order doesn't matter.

Hope it helps
• Why is 6 x 3 not right to find the number of combinations?