The number of ways selecting three numbers from 1 to 30, so as to exclude every selection of three consecutive number is:

The numbers of ways of selecting 3 number our of 30 is  30C3. But this include 28 ways of selecting 3 consecutive numbers. [viz (1, 2, 3), (2, 3, 4), 3, 4, 5),……,(28, 29, 30)]Thus, required number of ways is  30C3−28=4032.