The task is to distribute \( 500 \) distinct boxes evenly among \( 50 \) individuals, with each person receiving \( 10 \) boxes. To determine the number of ways this can be done, we use the following formula: \[ \frac{500!}{(10!)^{50}}. \] Explanation: - The total number of ways to arrange all the \( 500 \) distinct boxes is \( 500! \). - Each of the \( 50 \) individuals receives \( 10 \) boxes, and the internal arrangement of the boxes for each individual can be done in \( 10! \) ways. - Since there are \( 50 \) people, we need to divide by \( (10!)^{50} \) to account for the repeated arrangements among the boxes given to each person.
Final Answer: \[ \boxed{\frac{500!}{(10!)^{50}}} \]
Given, the function \( f(x) = \frac{a^x + a^{-x}}{2} \) (\( a > 2 \)), then \( f(x+y) + f(x-y) \) is equal to