Binomial Coefficient Calculator
Calculate nCr and nPr values with Pascal's triangle row visualization.
Inputs
Results
C(n, r)
120
P(n, r)
720
Pascal Row Length11
How to Use This Calculator
- Enter n (the total number of items) in the top field.
- Enter r (the number of items to choose) — must satisfy 0 <= r <= n.
- Review C(n, r) — the number of r-combinations — and P(n, r) — the number of r-permutations.
- Check the Pascal Row Length to see where C(n, r) falls in Pascal's triangle.
- Use these values in probability, combinatorics proofs, or algorithm analysis.
How the result changes with n (total)
| n (total) | C(n, r) | P(n, r) |
|---|---|---|
| 17 | 680 | 4,080 |
| 59 | 32,509 | 195,054 |
| 111 | 221,815 | 1,330,890 |
| 153 | 585,276 | 3,511,656 |
What each input means
- n (total)
- Total number of items (row of Pascal's triangle)
- r (choose)
- Number of items to choose (column in Pascal's triangle)
How this is calculated
Worked example, using the default values
- Identify Input Parametersn (total) = 10, r (choose) = 3 = 2 input(s) provided
- Calculate CC120 = 120
- Calculate PP720 = 720
- Calculate Pascal Row Length11 = 11
Engine last updated . Checked against 5 independently-derived tests — how we verify calculators.
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