How many distinct vectors (x1 , x2 , ..., xr ) can satisfy the constraints. Example: 8 identical blackboards are to be divided among 4 schools. Q (a): How many divisions are possible? Q (b): How many, if each school must receive at least 1 blackboard? From a group of 8 women and 6 men a committee consisting of 3 men and 3 women is to be formed. (a): How many different committees are possible? (b): How many, if 2 of the men refuse to serve together? (c): How many, if 2 of the women refuse to serve together? (d): How many, if 1 man and 1 woman refuse to serve together? Solution: (a): How many different committees are possible? = 56 (b): How many, if 2 of the men refuse to serve together? = 56 (c): How many, if 2 of the women refuse to serve together? = 50 (d): How many, if 1 man and 1 woman refuse to serve together?