Question

? Given: All US area codes are three-digit numbers that use the numerals 0 to 9. Step 2: How many area-codes are possible if the first digit can't be zero and no digit can be repeated? Use your keyboard and the keypad to enter your answer. Then click Done.

Answer 1

Answer: 648

Step-by-step explanation:

For the first slot, we have 9 digits to choose from (1 through 9).

Whatever we pick for the first choice, we have 9 choices left for the second slot. Say we picked 2 for the first slot. That means we have {0,1,X,3,4,5,6,7,8,9} to choose from. I used X to indicate we can't pick that digit any more. You'll see there are 9 items in that list.

Then for the third slot, we had 8 choices to pick from

Overall we have 9*9*8 = 81*8 = 648 different area codes possible where the first digit cannot be zero.