Question

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

Answer 1

Step-by-step explanation:

The number of ways of selecting four numbers from 1 to 30 without any restriction is

30

C

4

.

The number of ways of selecting four consecutive [i.e.(1,2,3,4),(2,3,4,5),....(27,28,29,30)] numbers is 27.

Hence, the number of ways of selecting four integers whichexcludes consecutive four selections is

=

30

C

4

−27=

24

30×29×28×27

−27=27378