Statistics Tool
Probability (nCr / nPr)
Calculate Combinations and Permutations.
Σ The Formula
nCr = n! / (r!(n-r)!) | nPr = n! / (n-r)!
Real World Examples
Combination (Lotto)
C(49, 6) = 13,983,816 ways to choose 6 numbers
Permutation (Race)
P(8, 3) = 336 ways to award Gold, Silver, Bronze
Committees
Choosing 3 members from 10: C(10, 3) = 120
Passwords
Arranging 4 different digits: P(10, 4) = 5,040
# About This Calculator
This calculator computes Combinations (nCr) and Permutations (nPr), two fundamental concepts in probability and combinatorics. Both calculate the number of ways to select r items from a set of n total items, but the key difference is Order.
Combinations (Order doesn't matter): Think of a fruit salad. Apples, Bananas, Grapes is the same salad as Grapes, Apples, Bananas. Order is irrelevant.
Key examples: Lottery numbers, poker hands, choosing a committee.
Permutations (Order matters): Think of a combination lock (ironically named). 4-2-7 works, but 7-2-4 does NOT. Order is crucial.
Key examples: Race winners (Golde, Silver, Bronze), passwords, seating charts.
Formulas
- Combination ($nCr$): $\frac{n!}{r!(n - r)!}$
- Permutation ($nPr$): $\frac{n!}{(n - r)!}$
How To Use
- Select **Combination (nCr)** if order doesn't matter (e.g., card hand).
- Select **Permutation (nPr)** if order DOES matter (e.g., race results).
- Enter **Total Items (n)**.
- Enter **Items to Choose (r)**.
- Click **Calculate**.
Frequently Asked Questions
What is the difference between nCr and nPr?+
Order! In Permutations (nPr), order matters (AB is different from BA). In Combinations (nCr), order does NOT matter (AB is the same as BA).
Can n be smaller than r?+
No. You cannot choose more items than you have available. 'n' must always be greater than or equal to 'r'.
What does '!' mean in the formula?+
It stands for Factorial. 5! = 5 × 4 × 3 × 2 × 1 = 120. It represents the number of ways to arrange objects.
How many ways to win the lottery?+
If you must pick 6 numbers from 49 (no order), it's a Combination: C(49, 6) = 13,983,816. Your chance is 1 in ~14 million.
Why is 0! equal to 1?+
It's a mathematical convention to make these formulas work. Conceptually, there is exactly one way to arrange zero items: by doing nothing.
Is Probability (nCr / nPr) free to use?+
Yes, Probability (nCr / nPr) on Matheric is completely free to use. We believe in accessible education and utility for everyone.