n choose k calculator n=240000, k=100 result

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) = (k n) = \frac{n !}{k ! ( n - k ) !} n = 240000 k = 100 C_{100} (240000) = (1 0 0 2 4 0 0 0 0) = \frac{2 4 0 0 0 0 !}{1 0 0 ! ( 2 4 0 0 0 0 - 1 0 0 ) !} \approx 1.101 \times 1 0^{380}

The number of combinations: 1.101950E+380

110195016596474398811
131965990565731459785138956648408192523640351861375969959790
176108452306318525911307207057067675301335286001696403428740
070384656391537518093193515599228656561813431116868192807427
100271801835058292881275639096760703995156780511411680690725
142097482573513093154252499648593498195443590590930790091849
689934524443930052818469614912170761422349125004814223237600

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

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

n choose k calculator n=240000, k=100 result

Calculation:

The number of combinations: 1.101950E+380

A bit of theory - the foundation of combinatorics

Combinations

Foundation of combinatorics in word problems