Question

7. How many different three-digit identification tags can be made if the first digit must be a 5 and repetitions are not permitted?

Answer 1

We have a three digit identification. Since the first number has to be 5 we have one option for the first slot. For the second digit we have 10 options (from 0 to 9) and finally for the last digit we have 9 options (since repetitions are not allowed). Then the number of options is (1)(10)(9)=90.