Number of  Arrangement

       
  Description  ( g >n )    
  Number of Balls (n)  
  Number of Boxes (g )  
  Number of Rooms 01  
   Find the total no. of Arrangements                                  
  As per Bose-Einstein Statistics ( Balls are indistinguishable )(n+g-1)! /(g-1)! (n!)  
  As per Fermi-Dirac Statistics (Balls are indistinguishable )   g! / n! (g-n)!  
  As per Maxwell-Boltzmann Statistics  (Balls are distinguishable ) gn  
       
       

Number of Arrangement ( Rooms more than 1)

           
    Total No. of Rooms (r)    
    Total No. of Boxes (g)    
    Total No. of Balls (n)  n=Σni    
     
    Room No.-- 1(r1) Room No. -- 2(r2) Room No.-- 3(r3)  
  No. of Boxes(gi)    gi > ni  
  No. of Balls(ni)  ( First click the check buttons before clicking submit)    
    

Find No. of Arrangements

  
  As per Bose-Einstein Statistics ( Balls are indistinguishable )(ni+gi-1)! /(gi-1)! (ni!)  
  As per Fermi-Dirac Statistics (Balls are indistinguishable )   gi! / ni! (gi-ni)!  
  As per Maxwell-Boltzmann Statistics  (Balls are distinguishable ) gini  
        (2nd click this)          n ! =                                                                              ni !  
    gini / ni !  
   

TOTAL NUMBER  OF ARRANGEMENTS

  
     
     
           
  As per Bose-Einstein Statistics ( Balls are indistinguishable ) Πi=1 to r (ni+gi-1)! /(gi-1)! (ni!)      
  As per Fermi-Dirac Statistics (Balls are indistinguishable )    Πi=1 to r gi! / ni! (gi-ni)!      
  As per Maxwell-Boltzmann Statistics  (Balls are distinguishable )    n! Πi=1 to r  [(gini) / (ni!)]