A function f: A→ B such that f (0) ≤ f (1) ≤ f(2) falls is one of the following four categories
Case 1 : f(0) < f(1) < f(2)
There are
C3 functions in this category
Case 2 : f(0) = f(1) < f(2)
There are
C2 functions in this catefory
Case 3 : f(0) < f(1) = f(2)
There are again
C2 functions in this category
Case 4 : f(0) = f(1) = f(2)
There are
C1 functions in this category
Thus, the number of desired functions is
C3+C2+C2+C1 =
C3+C2 =
C3