major credit cards such as visa or mastercard have a sixteen-digit account number of the form XXXX-XXXX-XXXX-XXXX. how many numbers of this type are possible?

Question

major credit cards such as visa or mastercard have a sixteen-digit account number of the form XXXX-XXXX-XXXX-XXXX. how many numbers of this type are possible?

anonymous · Answer

Well, you have 16 digits, and each of those can be the numeral 0-9, for 10 options apiece, so how can you find the total options?

anonymous · Answer

what i did was 9x16=144 but should i have done 10x16?

anonymous · Answer

(including those which start with 0's).

anonymous · Answer

ohhh ok, i never include 0 but i get why there are 10 choices but my answer would be 160 different ways

anonymous · Answer

I meant 10^16.  You'll have 10000000000000000 possibilities.

anonymous · Answer

why is it 10^16 instead of 10x16?

anonymous · Answer

You have 10 options for the first digit.  Then for the second digit, you have 10 options, but you can combine those with each of the 10 options for the first:
00, 01, 02, 03...
10, 11, 12, 13...
20, 21, 22, 23...
...
So if the number were only 2 digits there would be 10x10 = 100 ways to do it, but the number is 16 digits long...so there are 10x10x10...=10^16 ways.

anonymous · Answer

ok i get it! thank you for your help!