The number of odd numbers lying between 40000 and 70000 that can be made from the digits 0, 1, 2, 4, 5, 7 if digits can be repeated in the same number is

The numbers are of five digits having 4 or 5 in ten thousand’s place and 1 or 5 in unit’s place and the remaining digits are any of the given six digits.∴ Number of ways to fill ten thousand’s place =2P1=2Number of ways to fill unit’s place =2P1=2Number of ways to fill other three places = 63.∴ Required number of numbers = 2 × 2 × 63 = 864.