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## High school statistics

### Course: High school statistics>Unit 6

Lesson 6: Combinations

# Intro to combinations

Sal introduces the basic idea of combinations.

## 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)? • In How many ways can 5 letters be posted in 4 postboxes if each postboxes can contain any number of letters ? • How to remember the difference between combination and permutations? • Why is 6 x 3 not right to find the number of combinations? • Why is it FBC? What is FBC?
Why isn't it DBC? • this video helped sm, thanks sal! • At , I don't understand why I would have to divide by 6. I just don't understand where the 6 comes from and why. Someone please help me explain?

Thanks • When dealing with permutations, the order in which we pick the three people matters.

But when dealing with combinations, the order doesn't matter.

For example, 𝐴𝐵𝐶 and 𝐵𝐴𝐶 are different permutations, but not different combinations.

For each combination of three people, like 𝐴𝐵𝐶, we can construct six permutations. In this case they would be 𝐴𝐵𝐶, 𝐴𝐶𝐵, 𝐵𝐴𝐶, 𝐵𝐶𝐴, 𝐶𝐴𝐵 and 𝐶𝐵𝐴.

– – –

In the video, Sal finds that there are 120 possible permutations when choosing three people from a total of six people.

These 120 permutations can be divided into groups, such that each group consists of the permutations that represent the same combination.

Since we are choosing three people, each group would consist of 6 permutations.

Thereby there would be 120∕6 = 20 groups,
and because each group represents a unique combination, we can then conclude that the number of possible combinations when choosing three people from a total of six people is 120∕6 = 20.