n choose k calculator n=365, k=36 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 = 365 k = 36 C_{36} (365) = (3 6 3 6 5) = \frac{3 6 5 !}{3 6 ! ( 3 6 5 - 3 6 ) !} \approx 7.885 \times 1 0^{49} = 78858086928530368344422966400101919732616803114985

The number of combinations: 7.885808692853×10⁴⁹

78858086928530368344422966400101919732616803114985

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=365, k=36 result

Calculation:

The number of combinations: 7.885808692853×1049

A bit of theory - the foundation of combinatorics

Combinations

Foundation of combinatorics in word problems

The number of combinations: 7.885808692853×10⁴⁹