Combination
A combination is a selection of r items chosen from a set of n where order does not matter, calculated as n factorial divided by r factorial times (n − r) factorial.
See it move
A combination counts unordered selections, used when only group membership matters. Choosing an unranked group of 3 suppliers from 6 shortlisted, with no first, second or third distinction, gives C(6,3) = 6 factorial ÷ (3 factorial × 3 factorial) = 720 ÷ 36 = 20 possible groups. This is the permutation count divided by 3 factorial to remove every duplicate ordering of the same three suppliers.
The formula
Variables
- Total number of items available
- Number of items chosen (order not counted)
- Number of unordered groups
Counts the number of unordered groups of r items chosen from a set of n.
Check yourself
A hiring panel must choose an unranked committee of 4 members from 8 candidates. How many different committees are possible?