Question:

How many permutations or ways to pull a set (e.g. team) of size

*n*from a group of elements (e.g. people) of size

*k*.

Example #1: 3 people named A, B, C form permutations of a doubles tennis team.

AB, AC, BC makes 3 possible doubles team combinations.

Example #2: 4 people named A, B, C, D form permutations of a doubles tennis team.

AB, AC, AD, BC, BD, CD makes 6 possible doubles team combinations.

Example #3: 5 people named A, B, C, D, E form permutations of a three man basketball team.

ABC, ABD, ABE, ACD, ACE, ADE, BCD, BCE, BDE, CDE makes 10 possible team combinations.

How to formulate an equation to describe this situation? And how to solve it?

(Reworded) How many permutations of group size

*n*from group size

*k*?

So if there was a much larger set of people numbered in the hundreds, and you wanted to pull out a group to form teams or something, how many combinations could be formed? What is the general formula for such things?

So far I can figure it out with small numbers by running through the actual combinations, but have limited math skills and yet don't know how to describe this sort of thing with math symbols and formulas. I know this has something to do with factorial.

For pulling out a group of two members (say, for a doubles tennis team) I came up with this:

Example #1 above: n=2, k=3 and the actual combinations is 3. Maybe that is k!/2 = 6/2 = 3. So maybe some kind of pattern...?

Example #2 above: n=2, k=4 and the actual combinations is 6. Maybe that is k!/4 = 24/4 = 6. But where does this denominator come from...?

Following this idea, for n=2, k=5 and the actual combinations is 10. Maybe that is k!/12 = 120/12 = 10. But where does 12 come from...?

Or maybe I'm way off base...