How many numbers greater than a million can be formed with the digits 2,3,0,3,4,2,3.

To solve this problem, we need to consider the following steps:

1. Identify the number of digits: The digits given are 2,3,0,3,4,2,3. This means we have 7 digits to work with.

2. Identify the number of unique digits: The unique digits are 2,3,0,4. This means we have 4 unique digits.

3. Identify the number of times each unique digit is repeated: 2 is repeated twice, 3 is repeated three times, 0 is repeated once, and 4 is repeated once.

4. Determine the number of ways to arrange the digits to form numbers greater than a million: Since the number has to be greater than a million, the first digit (from the left) has to be either 2, 3, or 4. It cannot be 0.

   • If the first digit is 2 or 4, the remaining 6 digits can be arranged in 6!/(2!*3!) ways (6 factorial divided by the product of 2 factorial and 3 factorial). This accounts for the fact that the digit 2 is repeated twice and the digit 3 is repeated three times.

   • If the first digit is 3, we have two cases to consider. One where the second digit is 0 and one where the second digit is not 0. If the second digit is 0, the remaining 5 digits can be arranged in 5!/(2!*2!) ways. If the second digit is not 0, the remaining 5 digits can be arranged in 5!/(2!*2!) ways.

5. Add up the total number of ways: The total number of ways to arrange the digits to form numbers greater than a million is (2*6!/(2!3!)) + (25!/(2!2!)) + (35!/(2!*2!)) = 480 + 120 + 180 = 780.

So, there are 780 numbers greater than a million that can be formed with the digits 2,3,0,3,4,2,3.