Thread: Permutations and Combinations

How many sets of 3 numbers can be formed from the numbers {1,2,3,..,20} if no 2 consecutive numbers are set to be in a set?

The string “00001010000000100000”, three 1's & seventeen 0's, can be used to represent the subset {5,7,15}. In fact, any rearrangement of the string with no adjacent 1’s can represent a subset of three with no consecutive integers.
How many such rearrangements are there?