What is the key difference between nPr and nCr?

In nPr (Permutation), order matters (AB ≠ BA). In nCr (Combination), order does not matter (AB = BA). nCr always results in fewer possibilities than nPr.

What are real-world examples of Combinations?

Choosing lottery numbers, picking pizza toppings, selecting a committee, and drawing a poker hand.

Why is the Combination formula longer than the Permutation one?

The 'r!' in the denominator of the combination formula removes the different orders of the same items, as they are considered one group.

Are lottery odds based on Permutations or Combinations?

Combinations. In most lotteries, the order in which numbers are drawn does not matter; you just need to match the set of numbers.

Why is order irrelevant in a committee?

If you pick Alice and Bob for a group, it is the same committee whether you picked Alice first or Bob first.

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IPL 2026

Combination Calculator

Calculate item selections where order doesn't matter (nCr). Determine unique groups and subsets from a larger set.

Complete User Guide

Find combinations with these steps:

Step 1: Enter the total number of items (n).

Step 2: Enter the number of items to select (r).

Step 3: Click 'Calculate' to find the total unique groups.

Step 4: Use this when the order of selection is irrelevant (e.g., picking a team).

The Mathematical Formula

C(n, r) = n! / (r! * (n - r)!)

Combinations (nCr) are calculated when order is not important:

- **Formula**: C(n, r) = n! / (r! * (n - r)!) - **n**: Total items - **r**: Items selected - **!**: Factorial

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