Question

How many odd integers from 1000 to 8000 (inclusive) have distinct digits?​

Answer 1

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ANSWER

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

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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