- #1

Dr-NiKoN

- 94

- 0

How many distinct x tuples can be created using a subset of A?

Example:

|A| = 20

I want to know how many combinations of 7 tuples can be made from that set.

Example:

If A = {1 .. 20} three such combinations could be:

{1, 2}, {3, 4}, {5, 6}, {7, 8}, {9, 10}, {11, 12}, {13, 14}

{2, 1}, {4, 3}, {6, 5}, {8, 7}, {10, 9}, {12, 11}, {14, 13}

{20, 1}, {19, 2}, {18, 3}, {17, 4}, {16, 5}, {15, 6}, {14, 7}

The following is not another combination, since it's the same as the first one just with the tuples in a different order:

{13, 14}, {11, 12}, {9, 10}, {7, 8}, {5, 6}, {3, 4}, {1, 2}

My first tought was to just simply use: [tex]\frac{n!}{r!(n-r)!}[/tex] but that would include combinations like the last one. Where it's equivalent to the first, just with a different order.

How do I approach such a problem?