# Combination

## Keywords: combination without repetition with repetition

## Combination without Repetition

A combination is a way of selecting k items from a collection of n items (k ≤ n), such that (unlike permutations) the order of selection does not matter. The repetition of items is not allowed.

The number of combinations::

**Example:**

From 5 items {a,b,c,d,e} choose 2, repetition is not allowed:$${C}_{5}^{2}=\frac{5!}{2!\xb7(3)!}=(\genfrac{}{}{0ex}{}{5}{3})=10$$

(a,b), (a,c), (a,d), (a,e), (b,c), (b,d), (b,e), (c,d), (c,e), (d,e)## Combination without Repetition

A combination is a way of selecting k items from a collection of n items, such that (unlike permutations) the order of selection does not matter. The repetition of items is allowed.

The number of combinations:

**Example:**

From 4 items {a,b,c,d} choose 2 items, repetition is allowed:

The number of combinations: $${\overline{C}}_{4}^{2}=(\genfrac{}{}{0ex}{}{4+2-1}{2})=(\genfrac{}{}{0ex}{}{5}{2})=10$$

(a,a), (a,b), (a,c), (a,d), (b,b), (b,c), (b,d), (c,c), (c,d), (d,d)