Counting Methods [Formulas]

Factorial Design Counting Problem

Total Runs = (Level of Factor 1) × (Level of Factor 2)…….

Permutation Problem (repetition is allowed)

n^r

Each of the r positions can be filled by any of the n items.

Permutation Problem (repetition is not allowed)

P(n, r) = n!/(n - r)!

Used when arranging items and order matters

Combination Problem (repetition is allowed)

C(n + r - 1, r) = (n + r - 1)!/r!(n - 1)!

Use when the order doesn’t matter and items can repeat.

Combination Problem (repetition is not allowed)

C(n, r) = n!/r!(n - r)!

Used when order does not matter and no repetition is allowed.

Counting Principle Problem (repetition is allowed)

Total outcomes = n^r

Used when any of the steps have any of the same n outcomes again.

Counting Principle Problem (repetition is not allowed)

n!

Use when each choice reduces the options available for the next two steps.