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.
[tex]\frac{n!}{r_1!\times r_2!\times....\times r_n!}[/tex]Therefore, we will have;
[tex]\frac{8!}{3!\times2!\times2!}=\frac{8\operatorname{\times}7\operatorname{\times}6\operatorname{\times}5\operatorname{\times}4\operatorname{\times}3!}{3!\operatorname{\times}2\operatorname{\times}1\operatorname{\times}2\operatorname{\times}1}=8\operatorname{\times}7\operatorname{\times}6\operatorname{\times}5=1680[/tex]Answer: 1680 eight-digit codes
