Question

There are 6 boxes numbered 1,2.......6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is:

Answer 1

Answer:

The number of ways in which 1 green ball can be put =6 . The number of ways in which two green balls can be put such that the boxes are consecutive

=5 (i.e.,(1,2),(2,3),(3,4),(4,5),(5,6))

Similarly, the number of ways in which three green balls can be put

=4(i.e.(1,2,3),(2,3,4),(3,4,5),(4,5,6))

⋯⋯⋯⋯⋯ and so on.

∴ Total number of ways of doing this

=6+5+4+3+2+1=21

plz mark BRAINEST answer