There are 6 boxes numbered 1, 2,3,4,5 and 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 & the boxes containing green balls are consecutively numbered. The total no. of ways in which this can be done is?	Choices:
A) 18  B) 19  C) 21  D) 23  E) 25
If only one of the boxes has a green ball, it can be any of the 6 boxes. So, this can be achieved in 6 ways.   If two of the boxes have green balls and then there are 5 consecutive sets of 2 boxes. 12, 23, 34, 45, 56.   Similarly, if 3 of the boxes have green balls, there will be 4 options.   If 4 boxes have green balls, there will be 3 options.   If 5 boxes have green balls, then there will be 2 options.   If all 6 boxes have green balls, then there will be just 1 options.   Total number of options = 6 + 5 + 4 + 3 + 2 + 1= 
<gadget id="calculator">6 + 5 + 4 + 3 + 2 + 1</gadget>
<output>21</output>
21   21
<result>C</result>
There are 6 boxes numbered 1, 2,3,4,5 and 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 & the boxes containing green balls are consecutively numbered. The total no. of ways in which this can be done is?