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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

Combination formula for groupsNumbers 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. 

 

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 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 = formula to divide the items into 2 groups with unequal items    there are in total m + n items
  2. The number of ways to divide the items into m groups each containing n items =  Formula to divide items into groups with equal number of 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 = The number of ways to divide the items into m groups each containing n item with order being important   , 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 = formula to divide items into 3 groups with unequal items , please note the total number of items = m + n + p
  5.  Number of ways of dividing 3n things into three groups of n each = dividing items into 3 groups with equal no. of items , order of groups is NOT important
  6.  Number of ways of dividing 3n things into three groups of n each = Dividing items into 3 groups with order of importance

 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  = formula for dividing identical items into r groups
  • Number of ways distributing n identical items among r groups or person each one can have atleast one item = Number of ways distributing n identical items among r groups with 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 x ^rin the expansion = The number of ways of choosing objects

Some other equations are as follows

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

 

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