For each of $($a$)-($c$)$ below, either draw a graph with the specified properties or else explain why no such graph exists.

$($a$)$ Graph with six vertices of degrees $1,1,2,2,2,$ and $3.$

$($b$)$ Graph with four vertices of degrees $1,2,2,$ and $5.$

$($c$)$ Simple graph with five vertices of degrees $1,1,1,1,$ and $5.$