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  • How many ways can 9 identical balls be placed in three identical boxes?Option: 1 12Option: 2 <

How many ways can 9 identical balls be placed in three identical boxes?

Option: 1

12


Option: 2

36


Option: 3

72


Option: 4

None of these


Answers (1)

best_answer

We shall look into how many ways a sum of 9 can be achieved as a sum of three digits. Here are the patterns

  1. 9 = 9 + 0 + 0
  2. 9 = 8 +1 + 0 Here, 8 + 0 + 1 can not be considered as a separate pattern since its constituents 0, 1 and 8 are same; this is because, the three boxes are non-distinguishable.
  3. 9 = 7 + 2 + 0
  4. 9 = 7 + 1 + 1
  5. 9 = 6 + 3 + 0
  6. 9 = 6 + 2 + 1
  7. 9 = 5 + 4 + 0
  8. 9 = 5 + 3 + 1
  9. 9 = 5 + 2 + 2
  10. 9 = 4 + 4 + 1
  11. 9 = 4 + 3 + 2
  12. 9 = 3 + 3 + 3

Now, all the above twelve patterns will have only one way of formation each, just the way it is - since, all the 9 balls are non-distinguishable.

So, there are 12 ways available.

Posted by

chirag

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