Combination

• The number of possibilities to form an unordered subgroup
• Similar to arrangements, but unordered
• Also known as
• k-combination of n
• n choose k

Formula

• $n$: available number of elements
• $k$: total elements in the subgroup

$$\binom{n}{k} = \frac{n!}{(n-k)!*k!}$$ $$\binom{n}{k} = \frac{A_{n,k}}{k!}$$

Other symbols

$$\binom{n}{k} = C(n,k) = {n}C{k}$$

Example

• You have a set {1, 2, 3, 4} ($n = 4$) and you need to find all possible unordered subgroups of size 2 ($k = 2$), you would have the following subsets:
• 6 possibilities!

{1, 2}
{1, 3}
{1, 4}

{2, 3}
{2, 4}

{3, 4}