1. The problem asks for the number of permutations of the digits 5, 4, 3, and 2. 2. A permutation is an arrangement of all the members of a set into some sequence or order. 3. The formula for the number of permutations of $n$ distinct objects is: $$P_n = n!$$ where $n!$ (n factorial) is the product of all positive integers up to $n$. 4. Here, we have 4 digits, so $n = 4$. 5. Calculate $4!$: $$4! = 4 \times 3 \times 2 \times 1 = 24$$ 6. Therefore, there are 24 different permutations of the digits 5, 4, 3, and 2.