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Question Number 185350 by cortano1 last updated on 20/Jan/23
$$\:\:\:{C}_{\mathrm{4}} ^{\mathrm{4}} +{C}_{\mathrm{4}} ^{\mathrm{5}} +{C}_{\mathrm{4}} ^{\mathrm{6}} +...+{C}_{\mathrm{4}} ^{\mathrm{26}} \:=? \\ $$
Commented by mr W last updated on 24/Jan/23
$$={C}_{\mathrm{4}+\mathrm{1}} ^{\mathrm{26}+\mathrm{1}} ={C}_{\mathrm{5}} ^{\mathrm{27}} =\mathrm{80730} \\ $$$${generally}: \\ $$$$\underset{{k}={r}} {\overset{{n}} {\sum}}{C}_{{r}} ^{{k}} ={C}_{{r}+\mathrm{1}} ^{{n}+\mathrm{1}} \\ $$