question help: when three-digit area codes were introduced in...

Question

1.When three-digit area codes were introduced in 1947, the first digit had to be a number from 2 to 9 and the middle digit had to be wither 1 or 0. How many area codes were possible under this system?

Please explain in full detail if you can, thank you.

Answer 1

To state the question in full, we have that:

1. the first digit is from 2 to 9
2. the second digit is 0 or 1
3. the last digit is from 0 to 9

Then, the number of possible area codes is equal to the product of the number of options at each digit. Namely, for the first digit, there are 8 options, i.e. {2,3,4,5,6,7,8,9}; for the second digit, there are 2 options; for the third digit, there are 10 options, i.e. {0,1,2,3,4,5,6,7,8,9}. The number of possible area codes is 8*2*10=160.

Answer 2

Well 2-9 for the first digit, so 2 3 4 5 6 7 8 9, 8 possibilities

Middle digit 1,0 - so 2 possibilities

Last digit 0-9, so 10 possibilities

So 8 x 2 x 10 = 160 possibilities