Counting Principles and Permutation. A social security number consists of 9 digits. How many different social security numbers are possible if repetition of digits is permitted
If the lead digit can be a zero
then 10^9
If the lead digit cannot be a zero
then 9(10^8)
If the lead digit can be a zero
then 10^9
If the lead digit cannot be a zero
then 9(10^8)
To determine the number of different social security numbers possible, we can use the counting principle and permutation.
Since repetition of digits is permitted, each digit in the social security number can range from 0 to 9.
There are 10 options for each digit (0 to 9), and since there are 9 digits in the social security number, we can multiply these options together using the counting principle.
10 * 10 * 10 * 10 * 10 * 10 * 10 * 10 * 10 = 10^9
Therefore, there are 10^9 (10 raised to the power of 9) different social security numbers possible. This equals 1,000,000,000 different combinations.