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.

Combinations (Order doesn't matter): "My fruit salad has apples, bananas, and grapes." The order doesn't change the salad. Used for lottery numbers, committees, card hands. Formula: nCr = n! / (r!(n-r)!).

Permutations (Order matters): "The combination lock is 4-2-7." 7-2-4 won't open it. Used for races (1st, 2nd, 3rd place), passwords, seating arrangements. Formula: nPr = n! / (n-r)!.

This tool handles the factorials for you, allowing you to quickly solve counting problems without dealing with massive numbers manually.

How To Use

  1. Select Combination (nCr) or Permutation (nPr).
  2. Enter Total Items (n).
  3. Enter Chosen Items (r).
  4. View the total possible ways.

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. 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. It simply means there is 1 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.

About

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.

Combinations (Order doesn't matter): "My fruit salad has apples, bananas, and grapes." The order doesn't change the salad. Used for lottery numbers, committees, card hands. Formula: nCr = n! / (r!(n-r)!).

Permutations (Order matters): "The combination lock is 4-2-7." 7-2-4 won't open it. Used for races (1st, 2nd, 3rd place), passwords, seating arrangements. Formula: nPr = n! / (n-r)!.

This tool handles the factorials for you, allowing you to quickly solve counting problems without dealing with massive numbers manually.

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