Permutation اور Combination کیلکولیٹر (nPr, nCr)

نتائج

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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

متعلقہ کیلکولیٹرز

• Pascal مثلث اور binomial expansion (مراحل کے ساتھ)

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.