twelve balls are distributed among three boxes ,find the probability that the first box will contain 3 balls .... and also explain how we solve these type of prblms ....and sum stategy to make strong probability

Given, 12 balls are distributed among 3 boxes and we have to find out the probability that the first box will contain 3 balls.

Now, each ball can be put into any of the three mentioned boxes.

Therefore, total number of ways in which 12 balls can be put into 3 boxes = 3¹².

Again, out of 12 given balls, 3 balls can be choosen in ¹²C₃ ways.

Consider that the above choosen 3 balls are put into first box. So. the remaining 12 -3 = 9 balls are to be out in other two boxes. It can be done in 2⁹ ways.

Therefore, the total number of ways in which 3 balls are put in the first box and remaining 9 in other two boxes = ¹²C₃ × 2⁹ ways

Hence, the probability that first box will contain 3 balls  =

Tips:

In order to tackle such kind of problems firstly you should read the question statement 2-3 times and clear yourself what is being asked in the question and what is the correct procedure to find it? Once it is clear to you, you will easy solve any given problem.

Here, in the above question firstly we find the total number of probable cases then we find out the number of favourable cases according to the given conditions simply to find the required probability.