permutation n combination

Reva wrote:can anyone plz give me the right answer

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:

In future, please provide the choices and the source!

Let's break this up into 6 cases:

1 green ball, 5 red balls: 6 possible places for the green ball.

2 green balls, 4 red balls: the green balls can go in boxes 1/2, 2/3, 3/4, 4/5 or 5/6... that's 5 more possibilities.

3 green balls, 3 red balls: the green balls can go in boxes 1/2/3, 2/3/4, 3/4/5 or 4/5/6... that's 4 possibilities.

4 green balls, 2 red balls: the green balls can go in boxes 1/2/3/4, 2/3/4/5 or 3/4/5/6... that's 3 possibilities.

5 green balls, 1 red ball: the green balls can go in boxes 1/2/3/4/5 or 2/3/4/5/6... that's 2 possibilities.

6 green balls, 0 red balls: only 1 possibility.

So, there are 6+5+4+3+2+1 = 21 possible ways we can meet the requirements.

Of course, at some point (likely after the 2nd or 3rd step) we would have recognized the pattern and saved ourselves some grunt work.

first of all sorry for incomplete information second i want to thank for replying to my post explanation really helped me