Question

The number of ways in which 9 identical balls are place in three identical boxes? Timeline unavailable

Answer 1

Answer:

Number of ways = 12

Explanation:

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

9 = 9 + 0 + 0

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.

9 = 7 + 2 + 0

9 = 7 + 1 + 1

9 = 6 + 3 + 0

9 = 6 + 2 + 1

9 = 5 + 4 + 0

9 = 5 + 3 + 1

9 = 5 + 2 + 2

9 = 4 + 4 + 1

9 = 4 + 3 + 2

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.

Answer 2

Answer:12

Step-by-step explanation:(3c1×2c1×1c1)×2=12