CAT 2003 Slot 1 — QA Question 44
Each question is followed by two statements, A and B. Answer each question using the following instructions
Choose 1 if the question can be answered by using one of the statements alone but not by using the other statement alone.
Choose 2 if the question can be answered by using either of the statements alone.
Choose 3 if the question can be answered by using both statements together but not by either statement alone.
Choose 4 if the question cannot be answered on the basis of the two statements.
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
Answer & solution
- A
5
21
- C
33
- D
60
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Case 1: only 1 box with green ball.
Number of possible ways = 6
Case 2: 2 boxes with green balls
Table shows that the green balls are placed in the boxes which are consecutively numbered.
Number of possible ways = 5
Similarly,
Case 3: 3 boxes with green balls
Number of possible ways = 4
Case 4: 4 boxes with green balls
Number of possible ways = 3
Case 5: 5 boxes with green balls
Number of possible ways = 2
Case 6: 6 boxes with green balls
Number of possible ways = 1
∴ Total number of ways = 6 + 5 + 4 + 3 + 2 + 1 = 21
Hence, option (b).