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Question Number 101880 by mr W last updated on 05/Jul/20
$${Find}\:{the}\:{number}\:{of}\:{six}−{digit}\:{odd} \\ $$$${numbers}\:{without}\:{repeated}\:{digits}. \\ $$
Answered by bemath last updated on 05/Jul/20
$$\mathrm{5}×\mathrm{8}×{C}_{\mathrm{4}} ^{\mathrm{8}} ×\mathrm{4}! \\ $$
Commented by mr W last updated on 05/Jul/20
$${correct},\:{thanks}! \\ $$
Answered by som(math1967) last updated on 05/Jul/20
$$\mathrm{Odd}\:\mathrm{numbers}\:\mathrm{unitdigit}\:\mathrm{1} \\ $$$$\overset{\mathrm{9}} {\mathrm{p}}_{\mathrm{5}} −\overset{\mathrm{8}} {\:}\mathrm{p}_{\mathrm{4}} =\mathrm{9}×\mathrm{8}×\mathrm{7}×\mathrm{6}×\mathrm{5}−\mathrm{8}×\mathrm{7}×\mathrm{6}×\mathrm{5} \\ $$$$=\mathrm{8}×\mathrm{7}×\mathrm{6}×\mathrm{5}\left(\mathrm{9}−\mathrm{1}\right) \\ $$$$=\mathrm{8}×\mathrm{7}×\mathrm{6}×\mathrm{40} \\ $$$$\therefore\mathrm{total}\:\mathrm{odd}\:\mathrm{numbers}=\mathrm{56}×\mathrm{240}×\mathrm{5} \\ $$$$=\mathrm{67200} \\ $$
Commented by som(math1967) last updated on 05/Jul/20
$$\mathrm{welcome}\:\mathrm{sir} \\ $$
Commented by mr W last updated on 05/Jul/20
$${correct},\:{thanks}! \\ $$