Quick Answer – What are Permutations & Combinations?

Permutations count the number of ways to arrange r items from a set of n distinct items, where order matters. Combinations count the number of ways to select r items without regard to order. The formulas are nPr = n!/(n-r)! and nCr = n!/(r!(n-r)!), fundamental to probability and counting principles.

Key Formulas

Factorial: n! = n × (n-1) × ... × 1

Permutations: nPr = n! / (n-r)!

Combinations: nCr = n! / (r! (n-r)!) = nPr / r!

Solved Examples

Example 1: 7P3

7! / (7-3)! = 7! / 4! = 7×6×5 = 210

Example 2: 10C4

10! / (4! 6!) = (10×9×8×7) / (4×3×2×1) = 5040 / 24 = 210

Example 3: 6! = 720

Frequently Asked Questions

Q1. What if n or r is not an integer?

Both n and r must be non-negative integers. The calculator will show an error otherwise.

Q2. Can I compute nPr or nCr for large numbers?

Yes, up to n=170 safely. Beyond that, JavaScript cannot represent the factorial exactly and may show Infinity. For typical JEE/NCERT values, it works fine.

Q3. What happens if r > n?

By convention, nPr and nCr are zero when r > n. The calculator will display 0.

Q4. Is 0! really 1?

Yes, by definition 0! = 1. The calculator follows this convention.

Q5. How precise are the results?

Exact integer results for values within the safe range; large results may be shown in scientific notation if needed.

Permutations & Combinations Calculator