Step by Step Explanation
From the question, we are told that Shannon's birthdate is 02/29/1991. Generally, the number of digits present in her birth date is N = 8 and also we can see that 9 is repeated 3 times, 2 repeated 2 times and 1 is repeated 2 times.
Since this is a case of permutation with repetition we will use the formula below.
Therefore, we will have;
![(8!)/(3!*2!*2!)=\frac{8\operatorname{*}7\operatorname{*}6\operatorname{*}5\operatorname{*}4\operatorname{*}3!}{3!\operatorname{*}2\operatorname{*}1\operatorname{*}2\operatorname{*}1}=8\operatorname{*}7\operatorname{*}6\operatorname{*}5=1680]()
Answer: 1680 eight-digit codes