permutation/combination

vaibhav101 wrote:There are 6 boxes numbered 1 to 6. Each box is to be filled with either a red ball 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

A 5
B 21
C 33
D 60
E 54

Let us list down the total number of ways...

1. If only one of the 6 boxes has a green ball. So, we have 6 ways.
2. If any two of the 6 boxes have green balls, then the 5 consecutive sets of 2 boxes are 12, 23, 34, 45, 56.
3. If any three of the 6 boxes have green balls, then the 4 consecutive sets of 3 boxes are 123, 234, 345, 456.
4. If any four of the 6 boxes have green balls, then the 3 consecutive sets of 4 boxes are 1234, 2345, 3456.
5. If any five boxes of the 6 boxes have green balls, then the 2 consecutive sets of 5 boxes are 12345, 23456.
6. If all the 6 boxes have green balls, then there is only one way 123456

Total number of ways = 6 + 5 + 4 + 3 + 2 + 1 = 21.

The correct answer: B

Hope this helps!

-Jay
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