Question 1210169
<pre>

There are 6 non-increasing partitions of 5 with 4 addends 0 through 5. Below
each non-increasing partition are listed the possible distributions of white and
black balls possible in each case. 
 
1.      5 + 0 + 0 + 0 = 5
    WWBBB + 0 + 0 + 0 = 5

    1 way.

2.     4 + 1 + 0 + 0 = 5
    WBBB + W + 0 + 0 = 5
    WWBB + B + 0 + 0 = 5

    2 ways.

3.    3 +  2 + 0 + 0 = 5
    WBB + WB + 0 + 0 = 5
    WWB + BB + 0 + 0 = 5 
    BBB + WW + 0 + 0 = 5

    3 ways.

4.    3 + 1 + 1 + 0 = 5
    WBB + W + B + 0 = 5
    WWB + B + B + 0 = 5
    BBB + W + W + 0 = 5

    3 ways.

5.   2 +  2 + 1 + 0 = 5
    WW + BB + B + 0 = 5
    WB + WB + B + 0 = 5 
    WB + BB + W + 0 = 5

    3 ways.

6.   2 + 1 + 1 + 1 = 5
    WW + B + B + B = 5
    WB + W + B + B = 5
    BB + W + W + B = 5

    3 ways.

Total = 1 + 2 + 3 + 3 + 3 + 3 = 15 ways

Edwin</pre>