Six identical blue balls are put in three different boxes. What is he

Question

Six identical blue balls are put in three different boxes. What is he probability of putting balls in the boxes in equal numbers ?

(A) 1/28
(B) 1/21
(C) 1/8
(D) 1/7
(E) 1/6

Six blue balls are put in three boxes. The probability of putting balls in the boxes in equal numbers is

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Archit3110 · Answer

Total ways to put equal balls in 3 different boxes

n+1-rC r-1

6+1-3C 3-1

8c2 : 28 ways

There is only 1 way to put equal balls i.e. 2 in each so 1/28
Option A

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GmatPoint · Answer

Let the 3 different boxes be a, b, and c.
We know that a+b+c = 6, and a>=0, b>=0, c>=0.
Total number of combinations possible = n+r-1C r-1 , where n = number of balls, r = number of boxes
Thus, total possible cases = 8Cr = 8*7/2 = 28.

Since balls should be put equally, there is only one case possible where a=2, b=2 and c=2.
Thus, probability = 1/28.

vallequalle · Answer

Hello Sir, 
How did you get from 6+1-3C 3-1 to 8c2?
Thanks in advance

Navdeep2000 · Answer

The key thing to note in this question is that there is nothing in the prompt that states that we can't have a box with 0 balls. So, we have to consider that a possibility.

Let's list down the various possibilities i.e. various number of balls in 3 different boxes
(0,0,6) = (3!/2!) or 3
(0,1,5) = 3! or 6
(0,2,4) = 3! or 6
(0,3,3) = (3!/2!) or 3
(1,1,4) = (3!/2!) or 3
(1,2,3) = 3! or 6
(2,2,2) = (3!/3!) or 1

Let's now add up all the possibilities = (3+6+6+3+3+6+1) = 28 possibilities
Notice that there's only 1 way to have equal number of balls in all the 3 boxes

Applying the formula for probability: (Number of ways with equal number of balls in 3 boxes)/(Total number of ways 6 balls can be put in 3 boxes) or (1/28).

Option A

KarishmaB · Answer

Number of ways of putting 6 identical balls in 3 distinct boxes can be found by the partition method. 
We need all the arrangements of B B | B | B B B (Here, first box gets 2 balls, second box gets 1 ball and third box gets 3 balls) 
Number of arrangements =  \frac{8!}{6!*2!} = 28  (because 6 balls are identical and 2 partitions are identical)

If we were to put balls in the boxes in equal numbers, each box will get 2 balls. Since all balls are identical it doesn't matter which balls go in which box. So there is only 1 way of doing this.

Required probability = 1/28

Answer (A)

Six identical blue balls are put in three different boxes. What is he

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Six identical blue balls are put in three different boxes. What is he

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