BodhiAI

Nov. 15, 2019
Divison and Distribution of Objects Into Groups

A. Groups of Unequal Size

Number of ways in which (m+n+p) things can be divided into unequal groups containing m, n and p things is

Number of ways to distribute (m+n+p) things among 3 persons (as we can make a distinct between persons because no two persons are same) in the groups containing m, n and p things is

Here, 3! is for arranging the things in between 3 persons as no two persons are alike.

B. Groups Equal Size

I The number of ways of dividing (2m) different objects into two groups of m objects each when Distinction can be made between the groups is

II The number of ways of dividing (2m) different objects into two groups of m objects each when No Distinction can be made between the groups is

III In General, number of ways in which (mn) different things can be divided equally in n Groups is

{No Distinction}Number of ways in which (mn) different things can be distributed equally among n Different Persons

{Persons Distinct}