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 John and his amazing cooking skills./n(a) Consider the chefs with IDs ranging from p to q inclusive, where p ≤ q, and consider the

cooking slots with IDs ranging from r to s inclusive, where r ≤ 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.)