The number of ways in which $$16$$ identical things can be distributed among $$4$$ persons if each person gets at least $$3$$ things, is

Question

Infinity Learn · Accepted Answer

Required number $$=$$ coefficient of $$x16$$ in (x3$$ $$+$$ $$x4$$ $$+$$ … $$+$$ $$x7)4$$                             $$=$$ coefficient of $$x16$$ in $$x12$$ $$(1$$ $$+$$ x $$+$$ … $$+$$ $$x4)                           $$=$$ coefficient of $$x4$$ in $$1$$−$$x51$$−$$x4=$$ coefficient of $$x4$$ in $$1$$−$$x54(1$$−$$x)$$−$$4=$$ coefficient of $$x4$$ in $$1$$−$$4x5+6x10$$−…(1$$−$$x)−$$4=$$ coefficient of $$x4$$ in (1$$−$$x)−$$4=7C4=4$$⋅$$5$$⋅$$6$$⋅$$74$$!$$=35$$

The number of ways in which 16 identical things can be distributed among 4 persons if each person gets at least 3 things, is

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