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Question Number 56624 by pieroo last updated on 19/Mar/19

How many numbers greater than 2000  can be formed using the digits 1,3,4,5,6?  how many of these will be even?  repetition not allowed.

$$\mathrm{How}\:\mathrm{many}\:\mathrm{numbers}\:\mathrm{greater}\:\mathrm{than}\:\mathrm{2000} \\ $$$$\mathrm{can}\:\mathrm{be}\:\mathrm{formed}\:\mathrm{using}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{1},\mathrm{3},\mathrm{4},\mathrm{5},\mathrm{6}? \\ $$$$\mathrm{how}\:\mathrm{many}\:\mathrm{of}\:\mathrm{these}\:\mathrm{will}\:\mathrm{be}\:\mathrm{even}? \\ $$$$\mathrm{repetition}\:\mathrm{not}\:\mathrm{allowed}. \\ $$

Commented by pieroo last updated on 19/Mar/19

repetition not allowed. Thanks.

$$\mathrm{repetition}\:\mathrm{not}\:\mathrm{allowed}.\:\mathrm{Thanks}. \\ $$

Commented by Kunal12588 last updated on 19/Mar/19

repetion is allowed or not?  needed 4 or 5 or greater digit no?  if counting every number greater than 2000  formed using 1,3,4,5,6. answer ∞    counting 4 and 5 digit number, repetion  not allowed.  4×4!+5!=4!(9)=24×9=216 ans

$${repetion}\:{is}\:{allowed}\:{or}\:{not}? \\ $$$${needed}\:\mathrm{4}\:{or}\:\mathrm{5}\:{or}\:{greater}\:{digit}\:{no}? \\ $$$${if}\:{counting}\:{every}\:{number}\:{greater}\:{than}\:\mathrm{2000} \\ $$$${formed}\:{using}\:\mathrm{1},\mathrm{3},\mathrm{4},\mathrm{5},\mathrm{6}.\:{answer}\:\infty \\ $$$$ \\ $$$${counting}\:\mathrm{4}\:{and}\:\mathrm{5}\:{digit}\:{number},\:{repetion} \\ $$$${not}\:{allowed}. \\ $$$$\mathrm{4}×\mathrm{4}!+\mathrm{5}!=\mathrm{4}!\left(\mathrm{9}\right)=\mathrm{24}×\mathrm{9}=\mathrm{216}\:{ans} \\ $$

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