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Question Number 107844 by mr W last updated on 13/Aug/20
$${A}\:{general}\:{case}: \\ $$ $${we}\:{have}\:{totally}\:{n}\:{letters},\:{among}\:{them} \\ $$ $${n}_{\mathrm{1}} \:{times}\:{A},\:{n}_{\mathrm{2}} \:{times}\:{B},\:{n}_{\mathrm{3}} \:{times}\:{C}, \\ $$ $${n}_{\mathrm{4}} \:{times}\:{D}\:{etc}. \\ $$ $$\left({n}_{\mathrm{1}} ,{n}_{\mathrm{2}} ,{n}_{\mathrm{3}} ,{n}_{\mathrm{4},} ...\geqslant\mathrm{2},\:{n}>{n}_{\mathrm{1}} +{n}_{\mathrm{2}} +{n}_{\mathrm{3}} +{n}_{\mathrm{4}} +....\right) \\ $$ $${how}\:{many}\:{different}\:{words}\:{can}\:{be} \\ $$ $${formed}\:{using}\:{these}\:{n}\:{letters}\:{such}\:{that} \\ $$ $${same}\:{letters}\:{are}\:{not}\:{next}\:{to}\:{each} \\ $$ $${other}. \\ $$ $$ \\ $$ $${see}\:{also}\:{Q}\mathrm{107451}. \\ $$