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!)]