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# Probability & Statistics/Probability

Question
Hi how would I determine the difference between a permutation question and a combination method??

This is a very vague question about a basic idea, so I can only give a vague and basic answer.

A "permutation question" is a question in which the answer requires you to formulate some count -- counting the number of possibilities of some configuration, but the "permutation" part means that the order of the components of the configuration matters.

For example, if I asked you to choose 9 friends and line them up in a row, you would have to specify 9 friends but also tell me which is first, second, third, etc. when you put them in a row.

If I just asked you to form a group of 9 of your friends, with no arrangement or order, you only choose 9 friends. I don't care who is "first" (in fact, there is no "first"). This would be a combination instead.

In a permutation question, the order matters. The configuration you want to count has some specific ordering inherent (like people in a line). In a combination question, the order of the configuration is not relevant.

So, if you had 25 friends total, the answer to the first question would be "25P9" which is a way of writing "the number of permutations of 9 things from a set of 25." It can be computed as:

25! / (25 - 9)! = 25 × 24 × 23 × 22 × 21 × 20 × 19 × 18

The second question would have answer "25C9" which is a way to write "the number of combinations of 9 things from 25" and which is computed:

25! / [ 9! × (25-9)! ] = 25 × 24 × 23 × 22 × 21 × 20 × 19 × 18 / ( 9 × 8 × 7 × 6 × 3 × 4 × 3 × 2 × 1 )
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Probability & Statistics

Volunteer

#### Clyde Oliver

##### Expertise

I can answer all questions up to, and including, graduate level mathematics. I do not have expertise in statistics (I can answer questions about the mathematical foundations of statistics). I am very much proficient in probability. I am not inclined to answer questions that appear to be homework, nor questions that are not meaningful or advanced in any way.

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I am a PhD educated mathematician working in research at a major university.

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