What is the number of odd integers between 1000 and 9999 with no digit repeated?

Step-by-step solution

Case I When unit digit can be 1,3,5 or 7 & digit at thousand's place can be 1,2,3,4,5,6,7 or 8 . No. of ways digits can be filled are: array |l|l|l|l| 7 & 8 & 7 & 4 array Total no's =7 8 7 4=1568 . Case II When unit digit can be 9 & digit at thousand's place can be 1,2,3,4,5,6,7 or 8 . No. of ways digits can be filled are: array |l|l|l|l| 8 & 8 & 7 & 1 array Total no's =8 8 7 1=448 . Case III When unit digit can be 1,3,5 or 7 & digit at thousand's place can be 9 . No. of ways digits can be filled are: array |l|l|l|