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Both calculators run independently — change the inputs on either side to compare results.

Combinations and Permutations Calculator

Calculate combinations (nCr) and permutations (nPr), with or without replacement, for counting and probability problems. Use it for lottery odds, team selection, and combinatorics assignments.

Total Items (n) (items)

Items Selected (r) (items)

Calculation Type

With Replacement

Fill in the required fields to see your result.

Probability

Chi-Square Goodness of Fit Calculator

Tests whether your observed frequency counts match a theoretically expected distribution. Use it to check if a die is fair, verify that survey responses follow a predicted pattern, or validate a statistical model.

Observed Frequency 1 (observations)

Expected Frequency 1 (observations)

Observed Frequency 2 (observations)

Expected Frequency 2 (observations)

Fill in the required fields to see your result.

Key differences

	Combinations and Permutations Calculator	Chi-Square Goodness of Fit Calculator
Category	Probability	Probability
Inputs required	4	4
Result	Result (ways)	Chi-Square Statistic (χ²)
What it does	Calculate combinations (nCr) and permutations (nPr), with or without replacement, for counting and probability problems. Use it for lottery odds, team selection, and combinatorics assignments.	Tests whether your observed frequency counts match a theoretically expected distribution. Use it to check if a die is fair, verify that survey responses follow a predicted pattern, or validate a statistical model.