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How many ways can you choose four integers from the set {1; 2; 3; ...; 10} so that no two of them are consecutive?

Sagot :

These are the ways:
1 and 3, 1 and 4, 1 and 5, 1 and 6, .... 1 and 10, 2 and 4, 2 and 5, 2 and 6, 2 and 7, .... 2 and 10, 3 and 5, 3 and 6, 3 and 7, 3 and 8, ... 3 and 10, 4 and 6, 4 and 7, 4 and 8, 4 and 9, 4 and 10, 5 and 6, 5 and 7, 5 and 8, 5 and 9, 5 and 10, 6 and 8, 6 and 9, 6 and 10, 7 and 9, 7 and 10, 8 and 10. 
SO there are 7, 6, 5, 4, 3, 2, 1. There are 28 ways.