Question Number 20326 by kkr1729 last updated on 25/Aug/17
$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{positive}\:\mathrm{inegral} \\ $$$$\mathrm{solutions}\:\mathrm{of}\:\:\:{abc}\:=\:\mathrm{30}\:\mathrm{is} \\ $$
Commented by Tinkutara last updated on 25/Aug/17
$$\mathrm{30}\:=\:\mathrm{2}\:×\:\mathrm{3}\:×\:\mathrm{5}\:=\:\mathrm{8}\:\mathrm{factors} \\ $$$$\mathrm{Required}\:\mathrm{number}\:\mathrm{of}\:\mathrm{ways}\:=\:^{\mathrm{8}} {C}_{\mathrm{3}} \:=\:\mathrm{56} \\ $$$$\mathrm{Ordered}\:\mathrm{triplets}\:=\:^{\mathrm{8}} {P}_{\mathrm{3}} \:=\:\mathrm{336} \\ $$