An archaeology club has 59 members. How many different ways can the club select a president, vice president, treasurer, and secretary? There are $10,923,024$ different slates of candidates possible. (Simplify your answer.)

Step 1 ：This is a permutation problem. The number of ways to select a president, vice president, treasurer, and secretary from 59 members is given by the formula for permutations of n items taken r at a time, which is nPr = n! / (n-r)!. Here, n is the total number of items (59 members), and r is the number of items to select (4 positions).

Step 2 ：Let's denote the total number of members as n and the number of positions to be filled as r. In this case, n = 59 and r = 4.

Step 3 ：We can use the formula for permutations to calculate the number of different slates of candidates possible. The formula is nPr = n! / (n-r)!. Plugging in the values, we get 59P4 = 59! / (59-4)!

Step 4 ：The calculation gives us the number of permutations as 10,923,024.

Step 5 ：Final Answer: There are \(\boxed{10,923,024}\) different slates of candidates possible.