$(2$ pts$.$ each$)$ Answer these questions about the rooted tree illustrated.

$($a$)$ Which vertex is the root?

$($b$)$ Which vertices are internal?

$($c$)$ Which vertices are leaves?

$($d$)$ Which vertices are children of $j?$

$($e$)$ Which vertex is the parent of $h?$

$($f$)$ Which vertices are siblings of $o?$

$($g$)$ Which vertices are ancestors of $m?$

$($h$)$ Which vertices are descendants of $b?$

$(3$ pts$.)$ How many edges does a tree with $10,000$ vertices have?

$(5$ pts$.)$ A chain letter starts when a person sends a letter to five others. Each person who receives the letter either sends it to five other people who have never received it or does not send it to anyone. Suppose that $10,000$ people send out the letter before the chain ends and that no one receives more than one letter. How many people receive the letter, and how many do not send it out?