Question Number 56624 by pieroo last updated on 19/Mar/19
$$\mathrm{How}\:\mathrm{many}\:\mathrm{numbers}\:\mathrm{greater}\:\mathrm{than}\:\mathrm{2000} \\ $$$$\mathrm{can}\:\mathrm{be}\:\mathrm{formed}\:\mathrm{using}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{1},\mathrm{3},\mathrm{4},\mathrm{5},\mathrm{6}? \\ $$$$\mathrm{how}\:\mathrm{many}\:\mathrm{of}\:\mathrm{these}\:\mathrm{will}\:\mathrm{be}\:\mathrm{even}? \\ $$$$\mathrm{repetition}\:\mathrm{not}\:\mathrm{allowed}. \\ $$
Commented by pieroo last updated on 19/Mar/19
$$\mathrm{repetition}\:\mathrm{not}\:\mathrm{allowed}.\:\mathrm{Thanks}. \\ $$
Commented by Kunal12588 last updated on 19/Mar/19
$${repetion}\:{is}\:{allowed}\:{or}\:{not}? \\ $$$${needed}\:\mathrm{4}\:{or}\:\mathrm{5}\:{or}\:{greater}\:{digit}\:{no}? \\ $$$${if}\:{counting}\:{every}\:{number}\:{greater}\:{than}\:\mathrm{2000} \\ $$$${formed}\:{using}\:\mathrm{1},\mathrm{3},\mathrm{4},\mathrm{5},\mathrm{6}.\:{answer}\:\infty \\ $$$$ \\ $$$${counting}\:\mathrm{4}\:{and}\:\mathrm{5}\:{digit}\:{number},\:{repetion} \\ $$$${not}\:{allowed}. \\ $$$$\mathrm{4}×\mathrm{4}!+\mathrm{5}!=\mathrm{4}!\left(\mathrm{9}\right)=\mathrm{24}×\mathrm{9}=\mathrm{216}\:{ans} \\ $$