Question

7 indistinguishable balls are placed in 5 distinguishable cells find the probability that first cell is empty.
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Answer 1

Answer:

"This is the answer of your question"

Answer 2

First find the total outcome:

Each ball can go to any of the five cells in 5 ways. There are 5 balls. Therefore, the total outcome is 5*5*5*5*5=3125

Now, let us do the favorable cases. Only one cell has to be empty. This is possible only if we distribute the balls in this way (2, 1, 1, 1, 0). Since this is an arrangement, the empty cell can be any of the five cells. Total arrangement is 5!/3! = 20

Since the balls are distinct, we have to select the balls to be arranged in the said fashion.

First select 2 out of 5 balls in 5C2 or 10 ways.

Select 1 ball from the remaining 3 balls in 3C1 ways or 3 ways.

Select 1 ball from the remaining 2 balls in 2C1 or 2 ways.

Select 1 ball from the remaining 1 ball in 1 way

So the selection can be done in 10*3*2*1=60 ways.

Hence, the favorable cases are 20*60 = 1200

Required probability is 1200/3125 = 48/125