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CAT 2003 Slot 1 — QA Question 44

Permutation & CombinationEasy

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

Correct answer: 21

  • A

    5

  • 21

  • C

    33

  • D

    60

Solution

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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).

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CAT 2003 Slot 1 QA Q44: 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 — Solution | TheCATExam