In how many ways a seven digits odd number can be formed whose all the digits are distinct ?

A 7-digit odd number with all distinct digits: First digit (place 1): Can be 1-9 (not 0), so 9 choices. Last digit (place 7): Must be odd (1, 3, 5, 7, 9), so 5 choices. If first digit is odd, it's no longer available for the last digit. Digits 2, 3, 4, 5, 6: Each can be 0-9 excluding used digits, so 8, 7, 6, 5, 4 choices respectively. Case 1: First digit is odd (1, 3, 5, 7, 9) - 5 choices. Then last digit has 4 remaining odd choices. Middle 5 digits have 8, 7, 6, 5, 4 choices. Total for Case 1: 5 × 4 × 8 × 7 × 6 × 5 × 4 = 134400. Case 2: First digit is even (2, 4, 6, 8) - 4 choices. Then last digit has 5 odd choices. Middle 5 digits have 8, 7, 6, 5, 4 choices. Total for Case 2: 4 × 5 × 8 × 7 × 6 × 5 × 4 = 134400. Total = 134400 + 134400 = 268800. Option A is correct.