Question 1

Why is 0! = 1?

Accepted Answer

By convention and mathematical consistency. The number of ways to arrange zero objects is exactly one — the empty arrangement. This also makes the permutation and combination formulas work correctly at edge cases like C(n, 0) = 1.

Question 2

What is the difference between permutation with and without repetition?

Accepted Answer

Without repetition (standard nPr): once an item is selected it cannot be selected again. With repetition: each selection is independent and any item can appear multiple times. Example — a 4-digit PIN from digits 0–9 with repetition = 10^4 = 10,000. Without repetition = P(10,4) = 5,040.

Question 3

When do I use combination with repetition?

Accepted Answer

Use it when selecting from a set of types where you can pick the same type multiple times and order doesn't matter. Classic example: choosing 3 ice cream scoops from 5 flavors (you can repeat flavors). Answer: C(5+3−1, 3) = C(7,3) = 35.

Question 4

How large can n be before results become unreliable?

Accepted Answer

This calculator uses JavaScript BigInt for exact integer arithmetic, so results are mathematically precise for any n up to 1000. Beyond that, numbers have hundreds or thousands of digits and are displayed in scientific notation.

Question 5

What is a multiset permutation?

Accepted Answer

A multiset permutation counts arrangements of a collection where some objects are identical. For example, the word MISSISSIPPI has 11 letters with repetitions: M×1, I×4, S×4, P×2. Distinct arrangements = 11! ÷ (1! × 4! × 4! × 2!) = 34,650.

Question 6

What is the relationship between nCr and nPr?

Accepted Answer

nPr = nCr × r! — a permutation is a combination with the r selected items then arranged in all possible orders. Equivalently, nCr = nPr ÷ r!, dividing by r! removes the order.

Combinatorics Calculator