Number of ways in which 30 identical things are distributed among six persons is

Let person Pi get xi number of things such thatx1+x2+x3+x4+x5+x6=30If xi is odd or xi=2λi+1, where λi≥0, then2λi+λ2+λ3+λ4+λ5+λ6+6=30or λ1+λ2+λ3+λ4+λ5+λ6=12Then number of solutions is  12+6−1C6−1=17C5.  If xi is evenor xi=2λI, where λi≥1, then2λi+λ2+λ3+λ4+λ5+λ6=30or λi+λ2+λ3+λ4+λ5+λ6=15Therefore, required number of ways is  15−1C6−1=14C5.