Combination Formula

The number of combinations of n different things taken r at a time is given by

nCr = n! ⁄  r! (n-r)! ,0 < r ≤n

where,

  • n is the size of the set from which elements are permuted
  • r is the size of each permutation
  • ! is factorial operator

Combinations Formula with Examples

Combination is a way of selecting items from a collection of items in combination we do not look at the order of selecting items, but our main attention is on the total number of selected items from a given set of items. For example- suppose that we have three numbers say, a, b, and c. Then in how many ways we can select two numbers is known as a combination.

Table of Content

  • What is Combinations?
  • Combination Formula
  • Relation between Combination Formula and Permutation Formula
  • Difference between Permutations and Combinations
  • What is Factorial?

Similar Reads

What is Combinations?

Different groups that can be formed by choosing r things from a given set of n different things, ignoring their order of arrangement, are called combinations of n things taken r at a time....

Combination Formula

The number of combinations of n different things taken r at a time is given by...

Relation between Combination Formula and Permutation Formula

The main difference between combination and permutation is only that in permutation we also consider the order of selecting the things but in combination order of selection does not matter. And therefore, permutations are always greater than the combination....

Difference between Permutations and Combinations

Each of the arrangements that can be made out of a given set of things, by taking some or all of them at a time, are called Permutations. The order in which arrangements are taken is important in a Permutation....

What is Factorial?

Continued product of first n natural numbers (i.e., the product of 1, 2, 3, …, n) is denoted by symbol n! and read as factorial n....

Sample Questions

Question 1: Evaluate 4! – 3!...