Please tell question related to probability

Question

5 identical balls are distributed at random in 4 boxes named a,b,c& d find the probability that these boxes contains respectively 1,2,2,0 balls

Answer 1

A B C D  Let's tabulate possible distinct 'distributions'

5 0 0 0 ... one possibility

4 1 0 0 ... three possibilities

   0 1 0

   0 0 1

3 0 0 2 ... six possibilities

   0 2 0

   2 0 0

   1 1 0

   1 0 1

   0 1 1 

2 3 0 0 ... ten possibilities

   0 3 0

   0 0 3

   2 0 1

   2 1 0

   1 0 2

   1 2 0

   1 1 1

   0 1 2

   0 2 1 

I will let YOU tabulate all the possibilities where 1 goes into the A column. I predict there will be 15 of those!

Why? Because it appears that these counts are the TRIANGULAR numbers.

 

 

Do not fail to take note that I am leaving to you the final steps of tabulating/demonstrating all the possibilities that begin with 1 and 0 in the A position. Or better yet, discover a shortcut to computing that.

 

Ultimately, you'll have P(of the one event of interest) = 1/n where n is the total number of distinct distribution possibilities.