# Thread: Trouble Understanding the difference between permutations and Combinations and some sequence theories?

1. Ok so first question what is the difference between permutations amd combinations? second I don't under stand how to get a working formula for arithmitic, and geometriv series... can someone help me please?  2.

3. I will only address the first part of your O.P., because I do not understand the second part.

A permutation is: Originally Posted by Wolfram MathWorld
is a rearrangement of the elements of an ordered list into a one-to-one correspondence with itself. The number of permutations on a set of elements is given by A combination is: Originally Posted by Wolfram MathWorld
[t]he number of ways of picking unordered outcomes from possibilities.

I will illustrate these two concepts with an example:

Suppose I have a box. In this box, there are 4 balls. Each of them is labeled with a number (1 to 4).
A permutation would be a certain rearrangement of the balls in the box. One arrangement could be 1-2-3-4. Another one could be 1-3-2-4, or 4-2-1-3, etc. The number of permutations (or arrangements of the balls in the box) would be ( is in this case the number of balls: 4), thus: (as there are first four balls to pick from the box, then three, and so on)

A combination is merely picking balls at random from a total of balls in the box, thus: It should be noted that the balls are not replaced in the box in both cases.

Sources:
Permutation -- from Wolfram MathWorld
Combination -- from Wolfram MathWorld  4. Ok... So permutation is the number of orders outcomes while a combination (n choose m) just the number of possible out comes of n fitting into m?  5. Ok now my other question I know the equation for the sum of s=1+2+3+...n-1+n is equal to n(n+1) divided by 2 but I don't get how we get the equation. And what if the sequence was 1/2 + 2/2 + 3/2 +... N-1/2 + N\2? How do I fin the sum of that by making a formula?  6. Arithmetic series:        7. Originally Posted by KJW Arithmetic series:      Ok so the arithmetic and geometric formulas work for all?  8. Geometric series:         9. Thank you kwj and corito ergo sum.  10. Originally Posted by Physicsforall Ok... So permutation is the number of orders outcomes while a combination (n choose m) just the number of possible out comes of n fitting into m?

Yes, that is in essence what I have stated in post #2.  Bookmarks
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