Number of odd integers between 1000 and 8000 which have none of their digits repeated, is : (A) 1014 (B) 810 (C) 690 (D) 1736
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There are two restrictions operating this question.
1. For a number to be odd, the unit digit should be either 1,3,5,7 or 9.
2. Thousand can not be filled with 8 or 9. For unit digit when it is filled with 9, the thousands place can be filled in 7 ways.
Namely any digit from 1 to 7 the remaining two places can be filled in 8×7=56 ways.
∴Total no. formed in this way=56×7=392
Now if units place is filled with any of the four digits 1,3,5 or 7, the thousand′s place can be filled in 6 ways and the remaining two places can be filled in 8×7=56 Ways.
∴The total no. formed in the way=56×6×4=1344.
∴Total=392+1344=1736