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Permutation and Combination - Quant/Math - CAT 2009
CAT Sample Questions - Question 4 the day : June 1, 2004
The question for the day is from the topic Permutation and Combination.
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
| (1) |
5
|
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(2) |
21
|
| (3) |
33
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(4) |
60
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Correct choice - (2) Correct Answer -(21)
Explanatory Answer
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 = 21.
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