The digits 0 to 9 are used to form three digit codes; however, there

Hello, good explanation, thank you! I just noticed one small typo: When B is 9, C can have only 9 values (not 8).[/quote

Thanks mate. Overlooked.
It was a typo. Glad you noticed it !

My 2 cents on this:

The conditions are a great way to learn about arrangements. Based on the question there are a few conditions. Firstly, 0 to 9 equals 10 digitals. Remember that. Easy to take this for granted.

Firstly, the first digital possibilities are fixed as 8 given that both 0 or 9 cannot be the first digit (10-2)

Then on to the cases:

Case 1: when 2nd digit is 0

8 x 1 x 10 (1 being value of only 0, and 10 being all of the ones we can apply, including 9) = 80

Case 2: When 2nd digit is not 0, then 3nd and 3rd cannot both be 9

8 x 1 x 9 (1 being value of9, and since we have taken 9 as 2nd, then third cannot have a 9, so 10-1 = 9 ways) = 72

80 +72 = 152

A