Answer the following questions about a scheduling system for assigning chefs to cooking slots. Within the system, every single chef and every single cooking slot is assigned an integer ID. These IDs start with 1 and increment by 1. That is, if there is a chef with ID equal to 6, there must be chefs with IDs equal to 1, 2, 3, 4 and 5. The same restriction applies to the cooking slot IDs. Note that any cooking slot not assigned a chef will be covered by Sara and her amazing cooking
Answer the following questions about a scheduling system for assigning chefs to cooking slots. Within the system, every single chef and every single cooking slot is assigned an integer ID. These IDs start with 1 and increment by 1. That is, if there is a chef with ID equal to 6, there must be chefs with IDs equal to 1, 2, 3, 4 and 5. The same restriction applies to the cooking slot IDs. Note that any cooking slot not assigned a chef will be covered by Sara and her amazing cooking skills.
\begin{enumerate}
\item Consider the chefs with IDs ranging from $p$ to $q$ inclusive, where $p \leq q$, and consider the cooking slots with IDs ranging from $r$ to $s$ inclusive, where $r \leq s$. How many distinct functions for assigning these chefs to cooking slots are there? (The chefs are the domain and the cooking slots are the codomain.)
\item Consider the chefs and cooking slots with IDs ranging from $p$ to $q$ inclusive, where $p \leq q$. How many distinct functions for assigning chefs to cooking slots are there, such that every chef is assigned a cooking slot with an ID that is less than or equal to their ID?
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