Math & Trigonometry
Permutations Without and With Repetition (PERMUT & PERMUTATIONA Formulas)
Count ordered sequences without replacement using FACT(n) / FACT(n - k) and with replacement using POWER(n, k), plus compute no-repeat collision probabilities.
Ordered sequences: without replacement vs. with replacement
When order matters and each item can be used at most once—such as awarding Gold, Silver, and Bronze across 10 finalists—the count of ordered k-tuples is PERMUT(n, k) = n! / (n - k)!.
When items may repeat across positions—such as a k-digit keypad code drawn from n = 10 digits (0–9)—every position independently has n choices, giving PERMUTATIONA(n, k) = n^k = POWER(n, k).
| Pool Size (n) | Positions (k) | Without Repetition n!/(n-k)! | With Repetition n^k | Distinct-Only Share |
|---|---|---|---|---|
| 10 digits | 3 slots | 720 | 1,000 | 0.7200 |
| 10 digits | 4 slots | 5,040 | 10,000 | 0.5040 |
| 8 runners | 3 medals | 336 | 512 | 0.6563 |
| 5 symbols | 5 slots | 120 | 3,125 | 0.0384 |
Permutations Without Repetition (PERMUT Equivalent)
Computes FACT(n) / FACT(n - k) while guarding invalid inputs where k < 0 or k > n.
=IF(OR(B2 < 0, B2 > A2), "#NUM!", FACT(A2) / FACT(A2 - B2))Permutations With Repetition (PERMUTATIONA) & No-Repeat Share
POWER(A2, B2) counts ordered sequences allowing repeats; dividing distinct permutations by POWER(A2, B2) gives the exact probability that a random sequence has zero repeated elements.
=POWER(A2, B2)Try the example
Use the original values or change them to test your understanding.