Combination of TWO
===============

I have four basic numbers 1 2 3 4. If I have to make all possible
combinations of TWO out of these four basic numbers, then the answer
would be SIX =COMBIN(4,2).

I am planning to make unique sets out of these combinations. Since
there are four basic numbers, I will have to make a grid of 2 X 2
consisting all unique numbers which comes out to be THREE

1. 1-2 & 3-4 (All individual numbers in each set is unique)
2. 1-3 & 2-4
3. 1-4 & 2-3

If I have six basic numbers 1 2 3 4 5 6 and if I have to make all
possible combinations of TWO, then the answer would be FIFTEEN
=COMBIN(6,2)

If I make unique sets out of these combinations, I will have to make a
grid of 3 X 2 which comes out to be FIFTEEN

1. 1-2 & 3-4 & 5-6 (All individual numbers in each set is unique)
2. 1-2 & 3-5 & 4-6
3. 1-2 & 3-6 & 4-5
4. 1-3 & 2-4 & 5-6
5. 1-3 & 2-5 & 4-6
6. 1-3 & 2-6 & 4-5
7. 1-4 & 2-3 & 5-6
8. 1-4 & 2-5 & 3-6
9. 1-4 & 2-6 & 3-5
10. 1-5 & 2-3 & 4-6
11. 1-5 & 2-4 & 3-6
12. 1-5 & 2-6 & 3-4
13. 1-6 & 2-3 & 4-5
14. 1-6 & 2-4 & 3-5
15. 1-6 & 2-5 & 3-4

Combination of THREE
=================

I have six basic numbers 1 2 3 4 5 6. If I have to make all possible
combinations of THREE out of these six basic numbers, then the answer
would be TWENTY =COMBIN(3,3).

If I have to make unique sets out of these combinations. Since there
are six basic numbers, I will have to make a grid of 3 X 2 consisting
all unique numbers which comes out to be TEN

1. 1-2-3 & 4-5-6 (All individual numbers in each set is unique)
2. 1-2-4 & 3-5-6
3. 1-2-5 & 3-4-6
4. 1-2-6 & 3-4-5
5. 1-3-4 & 2-5-6
6. 1-3-5 & 2-4-6
7. 1-3-6 & 2-4-5
8. 1-4-5 & 2-3-6
9. 1-4-6 & 2-3-5
10. 1-5-6 & 2-3-4

If I have Nine basic numbers 1 2 3 4 5 6 7 8 9 and if I have to make
all possible combinations of THREE, then the answer would be EIGHTY
FOUR =COMBIN(9,3)

If I make unique sets out of these combinations, I will have to make a
grid of 3 X 3 which comes out to be 280

1. 1-2-3 & 4-5-6 & 7-8-9 (All individual numbers in each set is unique)
2. 1-2-3 & 4-5-7 & 6-8-9
..
..
..
..
..
..
280. 1-8-9 & 2-6-7 & 3-4-5

X------------X------ End of the problem ------X------------X

Answer for first scenario was 3
Answer for second scenario was 15
Answer for third scenario was 10
Answer for last scenario was 280

What I want to know is whether there is any mathematical/statistical
formula to calculate the result. I want to know is there any way to
derive the answer from any formula?

Sandy