How many odd three-digit integers greater than 800 are there such that all their digits are different? 72 40 56 81 104

IMO A Hundredth place either 8 or 9 Tenth place 0 to 9 Unit place 1,3,5,7,9 When Hundredth place is 8, Tenth place 0,2,4,6 (Not 8 as repeat), Unit place can be (1,3,5,7,9) = 1*4*5 = 20 Numbers When Hundredth place is 8, Tenth place 1,3,5,7,9, Unit place can be (1,3,5,7,9 except the current tenth one) = 1*5*4 = 20 Numbers When Hundredth place is 9, Tenth place 0,2,4,6,8, Unit place can be (1,3,5,7 Not 9) = 1*5*4 = 20 Numbers When Hundredth place is 8, Tenth place 1,3,5,7(not 9), Unit place can be (1,3,5,7,9 except the current tenth one and 9) = 1*4*3 = 12 Numbers Total = 20+20+20+12 = 72.

shovan85 wrote:IMO A Hundredth place either 8 or 9 Tenth place 0 to 9 Unit place 1,3,5,7,9 When Hundredth place is 8, Tenth place 0,2,4,6 (Not 8 as repeat), Unit place can be (1,3,5,7,9) = 1*4*5 = 20 Numbers When Hundredth place is 8, Tenth place 1,3,5,7,9, Unit place can be (1,3,5,7,9 except the current tenth one) = 1*5*4 = 20 Numbers When Hundredth place is 9, Tenth place 0,2,4,6,8, Unit place can be (1,3,5,7 Not 9) = 1*5*4 = 20 Numbers When Hundredth place is 8, Tenth place 1,3,5,7(not 9), Unit place can be (1,3,5,7,9 except the current tenth one and 9) = 1*4*3 = 12 Numbers Total = 20+20+20+12 = 72. Typo last [color = red]When Hundredth place is 8[/color] is not 8 its 9.