Consider the functions from 112 to 120 What is the number of

Consider the functions from {1,...,12} to {1,...,20}.

What is the number of functions f s.t. f(1) +···+ f(12) = 19? (Hint : set x_i = f(i). Is x_i 20 relevant?)

Solution

mapping is from  {1,...,12} to {1,...,20}. which means f(1) = 1 f(2) =2....f(12) = 12

so to calculate  f(1) +···+ f(12) = 19

the function applicaple will be f(1)+f(2)+f(4)+F(12) = 19

hence 4 functions