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p & c help plz

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p & c help plz

by quantskillsgmat » Wed Jan 25, 2012 3:42 am
There are 6 boxes numbered from 1 to 6.Each box is to be filled up either with red or green ball in such a way that atleast 1 box contains a green ball and boxes containing are consecutively numbered.The total number of ways in which this can be done is
a)5 b)21 c)33 d)60
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by Anurag@Gurome » Wed Jan 25, 2012 4:46 am
quantskillsgmat wrote:There are 6 boxes numbered from 1 to 6.Each box is to be filled up either with red or green ball in such a way that atleast 1 box contains a green ball and boxes containing are consecutively numbered.The total number of ways in which this can be done is
a)5 b)21 c)33 d)60
The least no. of green balls can be 1.
If there is 1 green and 5 red balls, then there are 6 ways of placing them in 6 boxes.
If there are 2 green and reaming 4 red balls, then this can be done in 5 ways.
If there are 3 green and 3 red balls, then this can be done in 4 ways.
If there are 4 green and 2 red balls, then this can be done in 3 ways.
If there are 5 green and 1 red ball, then this can be done in 2 ways.
If there are 6 green and 0 red balls, then this can be done in 1 way.

So, total no. of ways = 6 + 5 + 4 + 3 + 2 + 1 = 21 ways

The correct answer is B.
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by mankey » Wed Jan 25, 2012 10:02 am
Dear Anurag

Please explain this one further.

Regards.
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by ArunangsuSahu » Wed Jan 25, 2012 11:36 am
Let's Start with box 1
1
12
123
1234
123456
Total =6
******************
So If we start with 2 Total =5

Continuing in this way

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