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 ${ }^{30}{\mathrm{C}}_4.$ 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

${ }^{30}{\mathrm{C}}_4-27=\frac{30\times 29\times 28\times 27}{24}-27=27378$