# n choose k calculator

Find out how many different ways you can choose*k*items from

*n*items set without repetition and without order. This number is also called combination number or n choose k or binomial coefficient or simply combinations. See also general combinatorial calculator.

## Calculation:

$C_{k}(n)=(kn )=k!(n−k)!n! n=10k=4C_{4}(10)=(410 )=4!(10−4)!10! =4⋅3⋅2⋅110⋅9⋅8⋅7 =210$

### The number of combinations: 210

# A bit of theory - the foundation of combinatorics

## Combinations

A combination of a k-th class of n elements is an unordered k-element group formed from a set of n elements. The elements are not repeated, and it does not matter the order of the group's elements. In mathematics, disordered groups are called sets and subsets. Their number is a combination number and is calculated as follows:$C_{k}(n)=(kn )=k!(n−k)!n! $

A typical example of combinations is that we have 15 students and we have to choose three. How many will there be?

## Foundation of combinatorics in word problems

- Party

At the party, everyone clinked with everyone. Together, they clink $strng times. How many people were at the party? - Bits, bytes

Calculate how many different numbers can be encoded in a 16-bit binary word. - Orchard

10 trees in 5 lines grow in the orchard. How many trees are in the orchard? - Cards

How many ways can you give away 32 playing cards to 7 player?

more math problems »