How many different 3 digit numbers can be made from the digits 1 to 7 if repetition is not allowed and the number must be an odd number greater than 400

Question

I am not sure about the steps to get the answer

Answer 1

Okay, so the other one we just worked thorough.  Here, I'll give you the steps.,

 

For the first digit, how many digits among 1 to 7 are at least 4?

 

Note how many are even. Note how many are odd. These answers will affect the next calculation.

 

We know the last digit must be odd.  If the first digit is even, how many numbers are left that can go in the last slot that are odd? If the first digit is odd, how many numbers are left that can go in the last slot?

 

At this point, we will have used 2 out of 7,  so there will be five possibilities for digit two.

 

So, you take the number of odd first digits, times the number of remaining odd last digits, times five, then add the number of even first digits, times the number of odd last digits, times five, and that's your answer.