Explanation
The birth date of Shannon is 09/09/1990
Generally, the number of digits present in her birth date is n = 8
Looking at the date we can see that 0 is repeated 3 times and 9 is repeated 4 times. Therefore, the total number eight-digit code that she could make using her birthday given the total number of digits that make up her birth date is
[tex]n!=8![/tex]but given that digit, 0 repeated itself 3 times, and 9 repeated itself 4 times, then the total number of eight-digit codes that she could make using her birthday will be mathematically evaluated as
[tex]\frac{8!}{3!\times4!}=\frac{8\times7\times6\times5\times4!}{4!\times3\times2\times1}=8\times7\times5=280[/tex]Answer: 280
