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lets assume 6 boxes A,B,C,D,E,F

first two boxes can have k balls where  0≤k≤4

A+B=k

so Total ways of distributing n similar objects between r boxes  is $^{_{r-1}^{n+r-1}\textrm{C}}$

so $^{_{2-1}^{k+2-1}\textrm{C}}$ = $^{_{1}^{k+1}\textrm{C}}$ =(k+1)

now distribute remaining 10-k objects in the remaining 4 boxes

C+D+E+F=10-k

$^{_{3}^{13-k}\textrm{C}}$

now multiply both the terms and apply summation for k=0 to 4

$\sum_{k=0}^{4} (k+1)_{3}^{13-k}\textrm{C}$
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