Question 1022916: Ten distinguishable balls are distributed into 4 distant boxes such that a specified box contains exactly 2 balls.Find number of such distribution ?
A.3 power 8 B. 3 power 10
C.3 power 6. D.45*3 power 8
Found 2 solutions by robertb, Edwin McCravy:
Answer by robertb(5830)   (Show Source):
Answer by Edwin McCravy(20054)  (Show Source):
You can put this solution on YOUR website! Ten distinguishable balls are distributed into 4 distant boxes such that a specified box contains exactly 2 balls.Find number of such distribution ?
A.3 power 8 B. 3 power 10
C.3 power 6. D.45*3 power 8
We can choose the 2 balls to go in the specified box in 10C2 = 45 ways.
For every way that can be done, there are 8 balls left to
distribute among the other 3 boxes.
There are 3 decisions to make for each remaining ball.
Those 3 decisions are whether:
1. to place it in the first box, or
2. to place it in the second box, or
3. to place it in the third box.
So we have 3 possible decisions for the 1st remaining ball.
And for each of those,
we have 3 possible decisions for the 2nd remaining ball.
And for each of those,
we have 3 possible decisions for the 3rd remaining ball.
And for each of those,
we have 3 possible decisions for the 4th remaining ball.
And for each of those,
we have 3 possible decisions for the 5th remaining ball.
And for each of those,
we have 3 possible decisions for the 6th remaining ball.
And for each of those,
we have 3 possible decisions for the 7th remaining ball.
And for each of those,
we have 3 possible decisions for the 8th remaining ball.
So the answer is 45*3*3*3*3*3*3*3*3 = 45*3^8
Note: This allows the cases when some of the boxes are empty,
and even some cases where all the remaining balls are all in
one box.
Edwin
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