Total number of four digit odd numbers that can be formed using 0,1,2,3,5,7 (repetition allowed) are:
Solutions · 1
Official solution
Last digit must be odd: 1,3,5,7 (4 choices). First digit nonzero: since last digit is already fixed as one of the odd digits, first digit has 5 choices (0--5 minus 0, but including all 6 digits minus 0: actually 5 nonzero digits available including possibly the repeated odd one since repetition allowed): 5 choices. Middle two digits: 6 choices each (repetition allowed, any of the 6 digits).
\[\text{Total} = 5\times6\times6\times4 = 720\]