- permutation - refers to the different ways of arranging items from a set of objects, in a sequential order
- combination - refers to the different ways of choosing items from a set of objects, such that their order does not matter
|
Type |
Ordered? |
Replacement? |
Description & Formula |
|---|---|---|---|
|
Permutation WITH Replacement (𝑛𝑃𝑟𝑘) |
ORDERED |
REPLACEMENT |
the number of ways 𝑘 items can be selected from 𝑛 possible items WITH replacement after each selection (ORDERED)
|
|
Permutation WITHOUT Replacement (𝑛𝑃𝑘) |
ORDERED |
WITHOUT REPLACEMENT |
the number of ways 𝑘 items can be selected from 𝑛 possible items WITHOUT replacement after each selection (ORDERED)
|
|
Combination WITHOUT Replacement (𝑛𝐶𝑘) Binomial Coefficient (for Binomial Distribution) |
UNORDERED |
WITHOUT REPLACEMENT |
the number of ways 𝑘 items can be selected from 𝑛 possible items WITHOUT replacement after each selection (UNORDERED)
|
|
(𝑛𝐶𝑟𝑘) or ((𝑛𝐶𝑘)) |
UNORDERED |
REPLACEMENT |
the number of ways 𝑘 items can be selected from 𝑛 possible items WITH replacement after each selection (UNORDERED)
|
Totality
|
Totality Types |
Ordered? |
Replacement? |
Description & Formula |
|---|---|---|---|
|
Total Permutation (WITH Replacement) |
ORDERED |
WITH REPLACEMENT |
the number of ways 0 to 𝑛 items can be selected from 𝑛 possible items WITH replacement after each selection (ORDERED) 𝛴0≤𝑖≤𝑛[𝑃𝑟(𝑛,𝑖)] = 𝛴0≤𝑖≤𝑘[𝑛𝑖] = 𝑛0 + 𝑛1 + 𝑛2 + … + 𝑛𝑛 = (𝑛𝑛+1-1)/(𝑛-1) |
|
Total Permutation (WITHOUT Replacement) |
ORDERED |
WITHOUT REPLACEMENT |
the number of ways 0 to 𝑛 items can be selected from 𝑛 possible items WITHOUT replacement after each selection (ORDERED) 𝛴0≤𝑖≤𝑛[𝑃(𝑛,𝑖)] = 𝛴0≤𝑖≤𝑛[𝑛!/(𝑛-𝑖)!] = ? |
|
Total Combination (WITHOUT Replacement) |
UNORDERED |
WITHOUT REPLACEMENT |
the number of ways 0 to 𝑛 items can be selected from 𝑛 possible items WITHOUT replacement after each selection (UNORDERED) 𝛴0≤𝑖≤𝑛[𝐶(𝑛,𝑖)] = 2𝑛 |
|
Total Combination (WITH Replacement) |
UNORDERED |
WITH REPLACEMENT |
the number of ways 0 to 𝑛 items can be selected from 𝑛 possible items WITH replacement after each selection (UNORDERED) 𝛴0≤𝑖≤𝑛[𝐶𝑟(𝑛,𝑖)] = ? |