Combinations:

In last post I talked about calculating permutation. Combinaitons differ from permutation in that ordering does not matter in case of combinations. For example we were concerned about first digit, second digit etc, whereas in combination it will not matter. For example we need to pull 4 balls out of 10, order does not matter. To make it easy, let us say 2 balls are to be choosen out of 4

So we can choose

1,2
1,3
1,4
2,3
2,4
3,4

Total 6

Whereas when we were talking about permutation, we were concerned about order as well. So 1,2 was different from 2,1

1,2
1,3
1,4
2,1
2,3
2,4
3,1
3,2
3,4
4,1
4,2
4,3
Total 12, same as 4P2 or 4!/(4-2)!

So the difference between permutation and combination is that we have removed ordering info in case of combinations. In how many ways we can order 2 numbers, exactly 2 (1,2 or 2,1). In how many ways we can order 3 objects- 6 (1,2,3; 1,3,2; 2,1,3; 2,3,1; 3,1,2; 3,2,1) or 3!. Similarly we can prove n objects can be ordered n! times.

So a formula for combinations would be nPr/r!

nCr= nPr/n! or n!/(n-r)!r!

Using it for 4 balls out of 10
10!/4!6! = 210