Explanation:

How many odd three digit numbers can be formed using the numbers 0,1,2,3,4,5,6?
The first two places can only be filled by 3 and 5 respectively and there is only 1 way 
of doing this
Given that no digit appears more than once. Hence we have 8 digits remaining(0,1,2,4,6,7,8,9)
So, the next 4 places can be filled with the remaining 8 digits in 8P4 ways
Total number of ways = 8P4 = 8 x 7 x 6 x 5 = 1680