Let m ≥ n {\displaystyle {}m\geq n} . How many injective mappings do exist from { 1 , … , n } {\displaystyle {}\{1,\ldots ,n\}} to { 1 , … , m } {\displaystyle {}\{1,\ldots ,m\}} , and how many surjective mappings do exist from { 1 , … , n } {\displaystyle {}\{1,\ldots ,n\}} to { 1 , … , m } {\displaystyle {}\{1,\ldots ,m\}} ?
