You are correct that there are 10^8 possibilities for a string of 8 digits.
10 possibilities in position 1
10 possibilities in position 2
...
10 possibilities in position 8
10 * 10 * 10 * 10 * 10 * 10 * 10 * 10
Alternatively one can even simply observe that 99999999 is the highest number possible and since 00000000 is possible also then we have 99999999 + 1 different possibilities = 100000000 = 10^8
10 possibilities in position 1
10 possibilities in position 2
...
10 possibilities in position 8
10 * 10 * 10 * 10 * 10 * 10 * 10 * 10
Alternatively one can even simply observe that 99999999 is the highest number possible and since 00000000 is possible also then we have 99999999 + 1 different possibilities = 100000000 = 10^8