The book on combinatorial problems is presented to the reader in an entertaining, popular form. Nevertheless, it also deals with some rather complex combinatorial problems, gives a concept of the methods of recurrent relations and producing functions. The book includes several hundred combinatorics tasks taken by the author from various sources. Many tasks are borrowed from Whitworth's book "Choice and Chance" (Whitworth W. A. , Choice and Chance, London, 1901), books by Riordan, books by A. M. Yagloma and E. M. Yagloma "Non-elementary problems in elementary presentation", Gostekhizdat, 1954, various collections of problems of mathematical olympiads and t. d.