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Published on October 18th, 2012 In category Education | Maths

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Using combination formula for distribution of items in groups

Numbers of ways for distributing items into groups is one of the topic that is frequently asked in competitive exams. The items can similar or dis-similar and can be distributed into equal or unequal groups.

The given below formulas will help you to solve such problems very easily.

1. The numbers of ways to divide the items into 2 groups containing m items and n items =     there are in total m + n items
2. The number of ways to divide the items into m groups each containing n items =    , please note total no. of items will be m x n and order of groups IS NOT important
3. The number of ways to divide the items into m groups each containing n items =    , please note total no. of items will be m x n and order of groups IS important
4. Numbers of ways to divide the items into 3 groups with m, n & p items respectively is =  , please note the total number of items = m + n + p
5.  Number of ways of dividing 3n things into three groups of n each =  , order of groups is NOT important
6.  Number of ways of dividing 3n things into three groups of n each =

Distribution of identical items in groups

• Number of ways distributing n identical items among r groups or person each can have 0, 1 , 2 or more items  =
• Number of ways distributing n identical items among r groups or person each one can have atleast one item =
• The number of ways of choosing r objects from p objects of one kind, q objects of second kind, and so on is the coefficient of in the expansion =

Some other equations are as follows

• The number of non-negative integral solutions of the equation =
• The number of positive integral solutions of the equation =

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