- #1
Dr-NiKoN
- 94
- 0
Ok, given a set: A
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?
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?