Question Number 117567 by bounhome last updated on 12/Oct/20
$${give}\:{A}=\left\{{a},{b},{c},{d},{e}\right\};\:{n}\left({p}\left({A}\right)\right)=? \\ $$$$\:\:\: \\ $$
Answered by mr W last updated on 12/Oct/20
$${C}_{\mathrm{0}} ^{\mathrm{5}} +{C}_{\mathrm{1}} ^{\mathrm{5}} +{C}_{\mathrm{2}} ^{\mathrm{5}} +{C}_{\mathrm{3}} ^{\mathrm{5}} +{C}_{\mathrm{4}} ^{\mathrm{5}} +{C}_{\mathrm{5}} ^{\mathrm{5}} =\mathrm{2}^{\mathrm{5}} =\mathrm{32} \\ $$$$\Rightarrow{n}\left({p}\left({A}\right)\right)=\mathrm{32} \\ $$
Commented by bounhome last updated on 13/Oct/20
$${and}\:{p}\left({A}\right)=? \\ $$
Commented by mr W last updated on 13/Oct/20
$${all}\:\mathrm{32}\:{subsets}\:{of}\:{A}: \\ $$$$\left\{\mathrm{0}\right\} \\ $$$$\left\{{a}\right\},\left\{{b}\right\},...,\left\{{e}\right\} \\ $$$$\left\{{a},{b}\right\},\left\{{a},{c}\right\},...,\left\{{d},{e}\right\} \\ $$$$... \\ $$$$\left\{{a},{b},{c},{d},{e}\right\} \\ $$