Combination with repetition and no order. I'm looking for a way to calculate the number of combination of 10 choose 5 => $_5^{10}C$ while allowing any number repetitions and counting 12345 and 54321 only once (order isn't important, ie I count 11355 but not then 35115).
I think this number is majored by $10^5$, but how to remove ordering number ?

Since order doesn't matter, we can consider results as different if they differ after sorting.
In other words, when order doesn't matter, generate the results with inherent sorting.
If you build a table, 5 slots wide and 10 slots high, and trace all paths from bottom left to somewhere on the right edge, but only allow paths to go 1 step right and never go down, then a clear pattern emerges. The right hand side of this tabel contains 1,5,15,35.. or (n+3) choose 4. The sum at the right edge is 2002 or 14 ch 5.
The diagonals are Pascal's triangle.
