Combination with Repetition Table (nHr)
Enter a maximum n and a maximum r to build a reference table of nHr, the number of ways to choose r items from n types with repetition allowed. Values are computed exactly with BigInt.
Input
Enter a maximum n and a maximum r to list the values of nHr (combinations with repetition) in a table.
Largest n laid out across the top from 0
Largest r laid out down the side from 0
Result
Maximum n
8
Maximum r
8
Cells
81
Combinations with repetition nHr table
Columns are n, rows are r, and each cell is the value of nHr.
| r over n | n = 0 | n = 1 | n = 2 | n = 3 | n = 4 | n = 5 | n = 6 | n = 7 | n = 8 |
|---|---|---|---|---|---|---|---|---|---|
| r = 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| r = 1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| r = 2 | 0 | 1 | 3 | 6 | 10 | 15 | 21 | 28 | 36 |
| r = 3 | 0 | 1 | 4 | 10 | 20 | 35 | 56 | 84 | 120 |
| r = 4 | 0 | 1 | 5 | 15 | 35 | 70 | 126 | 210 | 330 |
| r = 5 | 0 | 1 | 6 | 21 | 56 | 126 | 252 | 462 | 792 |
| r = 6 | 0 | 1 | 7 | 28 | 84 | 210 | 462 | 924 | 1,716 |
| r = 7 | 0 | 1 | 8 | 36 | 120 | 330 | 792 | 1,716 | 3,432 |
| r = 8 | 0 | 1 | 9 | 45 | 165 | 495 | 1,287 | 3,003 | 6,435 |
Combinations with repetition are nHr = C(n plus r minus 1, r), computed exactly with BigInt.
How it works
- The number of combinations with repetition nHr counts how many ways you can choose r items from n types when repetition is allowed, and it equals C(n plus r minus 1, r).
- This table lists n across the top and r down the side, computing nHr for every value from 0 up to each chosen maximum.
- When r is 0 there is exactly 1 way (choose nothing), and when n is 1 there is exactly 1 way (pick the same item r times).
- Values are computed exactly with BigInt to avoid overflow, and the number of cells is capped so the table stays readable.
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Combination with Repetition Table (nHr)