Combination Table (Pascal's Triangle) Calculator
Enter a maximum n and see every nCr value for n from 0 up to that maximum, laid out as a lower-triangular table. It is Pascal's triangle at a glance.
Input
Builds a lower-triangular table of nCr (the number of ways to choose r items from n) for n from 0 up to the maximum you set.
Enter an integer between 0 and 30.
Result
Maximum n
8
Total cells
45
Largest value
70
Combination table (nCr)
Rows are n and columns are r. Each cell is nCr, and cells where r exceeds n are left blank.
| n \ r | r=0 | r=1 | r=2 | r=3 | r=4 | r=5 | r=6 | r=7 | r=8 |
|---|---|---|---|---|---|---|---|---|---|
| n=0 | 1 | ||||||||
| n=1 | 1 | 1 | |||||||
| n=2 | 1 | 2 | 1 | ||||||
| n=3 | 1 | 3 | 3 | 1 | |||||
| n=4 | 1 | 4 | 6 | 4 | 1 | ||||
| n=5 | 1 | 5 | 10 | 10 | 5 | 1 | |||
| n=6 | 1 | 6 | 15 | 20 | 15 | 6 | 1 | ||
| n=7 | 1 | 7 | 21 | 35 | 35 | 21 | 7 | 1 | |
| n=8 | 1 | 8 | 28 | 56 | 70 | 56 | 28 | 8 | 1 |
Symmetry
Each row is symmetric, so nCr equals nC(n-r)
Built from the previous row using nCr = (n-1)C(r-1) + (n-1)Cr, with the ends nC0 and nCn set to 1.
How it works
- Each row is built from the previous one using nC0 = nCn = 1 and the recurrence nCr = (n-1)C(r-1) + (n-1)Cr, which is Pascal's triangle.
- Values are computed with BigInt so large entries stay exact.
- The maximum n is intended to be between 0 and 30.
- Each row is symmetric, so nCr equals nC(n-r).
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Combination Table (Pascal's Triangle) Calculator