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

Let person  $P_i$ get  $x_i$  number of things such that
$x_1+x_2+x_3+x_4+x_5+x_6=30$
If  $x_i$  is odd or $x_i=2{\lambda }_i+1$ , where  ${\lambda }_i\ge 0$, then
$2({\lambda }_1+{\lambda }_2+{\lambda }_3+{\lambda }_4+{\lambda }_5+{\lambda }_6)+6=30$

or  ${\lambda }_1+{\lambda }_2+{\lambda }_3+{\lambda }_4+{\lambda }_5+{\lambda }_6=12$

Then number of solutions is  ${ }^{12+6-1}{C}_{6-1}={}^{17}{C}_5$. If  $x_i$ is even or  $x_i=2{\lambda }_I$, where  ${\lambda }_i\ge 1$, then

$$\begin{gathered} 2({\lambda }_1+{\lambda }_2+{\lambda }_3+{\lambda }_4+{\lambda }_5+{\lambda }_6)=30 \\ or {\lambda }_1+{\lambda }_2+{\lambda }_3+{\lambda }_4+{\lambda }_5+{\lambda }_6=15 \end{gathered}$$

Therefore, required number of ways is  ${ }^{15-1}{C}_{6-1}={}^{14}{C}_5$