N Choose K Calculator n=100, k=50 result

Find out how many different ways you can choose k items from a set of n items 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) = (k n) = \frac{n !}{k ! ( n - k ) !} n = 100 k = 50 C_{50} (100) = (5 0 1 0 0) = \frac{1 0 0 !}{5 0 ! ( 1 0 0 - 5 0 ) !} \approx 1.008 \times 1 0^{29} = 100891344545564193334812497256

The number of combinations: 1.0089134454556×10²⁹

100891344545564193334812497256

A bit of theory - the foundation of combinatorics

Combinations

A combination of the 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 the order does not matter. In mathematics, such unordered groups are called sets and subsets. The count is called a combination number and is calculated as follows:

C_{k} (n) = (k n) = \frac{n !}{k ! ( n - k ) !}

A typical example: we have 15 students and need to choose 3. How many ways can this be done?

N Choose K Calculator n=100, k=50 result

Calculation:

The number of combinations: 1.0089134454556×1029

A bit of theory - the foundation of combinatorics

Combinations

Foundation of combinatorics in word problems

The number of combinations: 1.0089134454556×10²⁹