Person A randomly selects 4 distinct numbers from the set \( \{1,2,3,4,5,6,7,8,9\} \) and arrang...

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Person A randomly selects 4 distinct numbers from the set \( \{1,2,3,4,5,6,7,8,9\} \) and arrange them in descending order to form a 4 digit number and person \( B \) randomly selects 4 distinct numbers from set \( \{1,2,3,4,5,6,7,8\} \) and also arranges them in descending order to form a 4 digit number. Then which of the following is/are correct?
(a) Probability that person As 4 digit number is greater than person Bs number is \( \frac{{ }^{8} C_{3}}{{ }^{9} C_{4}}+\frac{1}{2}\left(1-\frac{1}{{ }^{9} C_{4}}\right) \)
(b) Probability that person A and B have same 4 digit number is \( \frac{1}{{ }^{9} C_{4}} \)
(c) Probability that person As 4 digit number is greater than person Bs number is \( \frac{2 \cdot{ }^{8} C_{3}+{ }^{8} C_{4}-1}{2 \cdot{ }^{9} C_{4}} \)
(d) Probability that person \( A \) and \( B \) have same 4 digit number is \( \frac{{ }^{8} C_{4}}{{ }^{9} C_{4}} \)
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