SOLUTION: Each of 9 different books is to be given at random to Rebecca, Sheila, or Tom. What is the probability that Rebecca receives 2 books, Sheila receives 4, and Tom receives 3?

1.  First of all, let me note/clarify that the condition does not prohibit that all 9 books go to Rebecca.

    It also  does not prohibit that all 9 books go to Sheila.

    It also does not prohibit that all 9 books go to Tom.


    Then the total number of different ways to distribute 9 books between 3 persons is .


    To better understand why it is so, imagine, that the teacher observes this process and write to his notebook to whom of the three persons

    the current book goes. He write "R" if the book goes to Rebecca; writes "S" if the book goes to Sheila; and write "T" if the book goes to Tom.


    So, for each way of distribution of 9 books the teacher has written the word of the length 9, consisting of 3 letters R, S and/or T.


    Repetitions are allowed - so the number of such words is , as I said above.



2.  Now we can select 2 books for Rebecca from 9 books by  =  = 36 ways.

    We can select 4 books for Sheila from remaining (9-2) = 7 books by  =  = 35 ways.

    As soon as the books for Rebecca and for Sheila are selected, Tom will take the remaining books - he has no choice.



3.  Therefore, the probability under the question is equal to   = 0.064 = 6.4%.