Previous in Permutation and Combination Next in Permutation and Combination
Question Number 111937 by bemath last updated on 05/Sep/20
Answered by bobhans last updated on 05/Sep/20
$$\:\mathrm{let}\:\mathrm{the}\:\mathrm{first}\:\mathrm{five}\:\mathrm{question}\:\mathrm{is}\:\mathrm{number}\::\: \\ $$$$\mathrm{1};\:\mathrm{2};\:\mathrm{3};\:\mathrm{4};\:\mathrm{5}\: \\ $$$$\mathrm{case}\left(\mathrm{1}\right)\:\Rightarrow\:\mathrm{C}\:_{\mathrm{4}} ^{\mathrm{5}} \:×\:\mathrm{C}\:_{\mathrm{4}} ^{\mathrm{5}} \:=\:\mathrm{25}\: \\ $$$$\mathrm{case}\left(\mathrm{2}\right)\Rightarrow\:\mathrm{C}\:_{\mathrm{5}} ^{\mathrm{5}} \:×\:\mathrm{C}\:_{\mathrm{3}} ^{\mathrm{5}} \:=\:\mathrm{1}×\mathrm{10}=\mathrm{10} \\ $$$$\mathrm{totally}\:\mathrm{25}\:+\mathrm{10}\:=\:\mathrm{35}.\: \\ $$