# How to Calculate Permutations and Combinations

Yesterday's post showed how to tell the difference between permutations and combinations. The day before, I posted about n! and what the heck to do with it. Now you're ready to do some calculations.

Here're the two formulas and how they compare:

And here are the numbers worked out from the video above:

Here's an application of it using the cat example from the first video of yesterday's post:

Post your questions and thoughts in the comments section.

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2 Responses to How to Calculate Permutations and Combinations
1. maria

hi
In the question: "in how many ways can 4people be seated in a row of 12 chairs?"
how can i tell of its a permutation or combination?

• Bon

Thanks for your question, Maria.

The real question turns out to be one of these:

You have 12 chairs in a row. How many ways can you pick four of them to have four different people sit in? (permutation)
OR
You have 12 chairs in a row. How many ways can you pick four of them to have people sit in? (combination)

Explanation:

It sometimes helps if you think about an example. Say your four different people are Adam, Betty, Carl and Diane. Now consider a few possible ways they can sit in that 12-chair row.

ABCDxxxxxxxx
BACDxxxxxxxx
xABCDxxxxxxx
xBACDxxxxxxx
AxBCDxxxxxxx
BxACDxxxxxxx

These are only a few. But look at the first two. Those look different. And indeed Betty might really be into Carl, so she'd definitely argue that they're different. If you consider them different, then it is permutation.

Now supposed we don't care that the people are different. The question then is, "How many ways can you pick four chairs to have people sit in?" The above examples now look like this:

PPPPxxxxxxxx
PPPPxxxxxxxx
xPPPPxxxxxxx
xPPPPxxxxxxx
PxPPPxxxxxxx
PxPPPxxxxxxx

So now it's clear that this is a combination - because the chairs are merely being occupied by some human (no preference, order or importance as to whom actually gets their heiney into the seat).

So really, the question is - how do you interpret the original question?