Combination

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:

Cnk=n·(n1)·(n2)·...(nk+1)k!
Cnk=n!k!·(nk)!=(nk)

Example:

From 5 items {a,b,c,d,e} choose 2, repetition is not allowed:C52=5!2!·(3)!=(53)=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:

C¯nk=(n+k1k)

Example:

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

The number of combinations: C¯42=(4+212)=(52)=10

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

Keywords: combination without repetition with repetition