If I wanted the different 3-card possible combinations from a total of 4 cards in ascending order, I would have:
$(1,2,3)$
$(1,2,4)$
$(1,3,4)$
$(2,3,4)$
EIDT:
How can I get all the possible, unique triplets in ascending order given an arbitrarily selected subset of cards from a standard deck of 52 cards?
I was misunderstanding the problem. Here's a bigger example, I'm given the cards:
$6, 1, 4, 3, 2, 4, 5$
- I can have more than one card with the same number, but each triplet cannot contain repeated numbers.
- Each triplet has to be in ascending order, but within the constraints of the original order.
In this example, the number 6 cannot appear in any triplet.
The first 4 isn't going to appear in any triplet either, but the second 4 allows to form (1,4,5). The results are:
$(1,4,5)$
$(1,2,4)$
$(1,2,5)$
$(3,4,5)$
$(2,4,5)$
With these restrictions in place, it's probably not a combinatorics problem.
Best Answer
Hint: for any triplet there are $6$ orders and you accept $1$. Do you want the number of them or a list. The list will be too large for most purposes.