Answer:
The solution can be broken into 2 steps:
The first will be to have all variations with the first digit being 2. So the variations for the First digit x1 can be one only and that is 1. The variation for the second digit x2 can be either 3, 5, or 6 as 2 is already taken and 1 cannot be as the 5 digit number should be greater than 23000. The variation for the third digit can be the other 3 digits possible. So x3 is 3. The variation for the fourth digit can be the other 2 digits. Do x4 is 2. The variation of the fifth digit is left to be 1. So x5 is 1. So total combinations are 1*3*3*2*1=18.
The first digit can be 3, 5, or 6 as 1 is not allowed and 2 is taken. So x1 is 3. x2 is the other 4. x3 is 3. x4 is 2 and x1 is 1. So the combinations are 3*4*3*3*1=72.
Explanation: