Permutation اور Combination کیلکولیٹر (nPr, nCr) — مرحلہ وار

Mode

Combination (nCr) Permutation (nPr) Factorial (n!)

n (integer ≥ 0)

r (0 ≤ r ≤ n)

Precision

Exact Approx

Show steps ٹیچر موڈ

نتائج

Exact value: —

Digits: —

Scientific notation: —

Step log

Steps are hidden. Turn on “Show steps” to view them.

استاد کے نوٹس

Combination: nCr = n! / (r!(n-r)!). Symmetry C(n, r) = C(n, n-r) lets you halve the work by using k = min(r, n-r).
Permutation: nPr = n! / (n-r)!. Remember P(n, 0) = 1 and P(n, n) = n! for boundary checks.
Factorial: n! = 1 × 2 × … × n with 0! = 1. Reinforce the base case when reviewing recurrence proofs.
When ان پٹ اقدار blow past the Exact limit (roughly n = 10,000), switch to Approx so learners still see the order of magnitude and digit count.
This tool is for educational use only. Always double-check final answers before grading or publishing materials.

عمومی سوالات

کیا ہے the difference between permutations and combinations?

Permutations treat the order of selection as unique (AB ≠ BA). Combinations treat those as the same outcome, counting only distinct subsets.

کب I switch between Exact and Approx?

Use Exact for values within the BigInt range (up to about n = 10,000 with k ≤ 5,000). Switch to Approx when the exact integer would be too large; you will still see the digit count and an accurate scientific notation.

حساب کیسے کیا گیا

Combinations nCr and permutations nPr with factorials.
For large n uses logs/approximation to avoid overflow.
URL (ویب پتہ) شیئر کریں preserves n and r.

نتائج

Step log

عمومی سوالات

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