The number of ways in which we can select four numbers from 1 to 30 so as to exclude every selection of four consecutive numbers is

The number of ways of selecting four numbers from 1 to 30 without any restriction is  30C4. The number of ways of selecting four consecutive [i.e. (1,2, 3, 4), (2, 3, 4, 5), ..., (27,28,29, 30)] number is 27. Hence, the number of ways of selecting four integers which excludes consecutive four selections is  30C4−27=30×29×28×2724−27=27378