n choose k calculator n=487, k=9 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 = 487 k = 9 C_{9} (487) = (9 4 8 7) = \frac{4 8 7 !}{9 ! ( 4 8 7 - 9 ) !} = \frac{4 8 7 \cdot 4 8 6 \cdot 4 8 5 \cdot 4 8 4 \cdot 4 8 3 \cdot 4 8 2 \cdot 4 8 1 \cdot 4 8 0 \cdot 4 7 9}{9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1} = 3941897198136002820

The number of combinations: 3941897198136002820

3941897198136002820

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: