Combinations (binomial coefficient)

\binom{n}{k}=\dfrac{n!}{k!(n-k)!}

Result unit: — (liczba)

What it describes

The number of k-element subsets of an n-element set (order does not matter).

n

number of elements

k

size of the selection

Choosing k elements from n with order irrelevant — we divide the variations by

k!

(the number of arrangements of the chosen elements). This is the binomial coefficient.

Draws, teams, selections without order (lottery, committees).

How many 2-person pairs can be formed from 5 people?

Substitution

n=5

k=2

Result

\binom{5}{2}=10

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