Question 1160018
<br>
The "stars and bars" method used by another tutor is a good tool for problems like this where the numbers are larger, and where there are no restrictions on how large the numbers can be.<br>
However, direct use of the stars and bars method for this problem gives a wrong result, because the integers are restricted to the range 1 to 6 inclusive. So counting the number of ways by enumeration is necessary.<br>
I would assume, unlike one of the other tutors, that, for example, 1+3+5 is a different result than 3+1+5....<br><pre>
  combinations    number of
   with a sum   permutations
     of 9
  --------------------------
    1+2+6         3! = 6
    1+3+5         3! = 6
    1+4+4      3!/2! = 3
    2+2+5      3!/2! = 3
    2+3+4         3! = 6
    3+3+3      3!/3! = 1
  ------------------------
            total:    25<pre><br>
ANSWER:  There are 25 ways for the sum of the numbers on the three people's dice to be 9.<br>