How this tree has 6 subtress?

Question

I have got a graph theory question from a friend as follows:

It is a tree as shown below rooted at "a". And asks me to find the number of subtrees it has.

I have found 5 subtrees as marked in red cirles. He says, it is 6. Am I missing any possible subtree, which by definition is a subtree?

Thanks.

Updated: Definition of subtree -

Subtree is a non-empty subgraph satisfying the following condition: For any vertex x, if x belongs to subtree P, then the parent of x also belongs to P. Note that each subtree contains the root.

Answer 1

By your definition, there are actually nine subtrees: $$abcde,abde,ade,abcd,abd,ad,abc,ab,a$$ This can be understood by considering at which points the subtree branches stop at, for each branch of the original tree. For the left branch we have a choice in $A=\{a,b,c\}$ and for the right one we have a choice of $B=\{a,d,e\}$. The nine trees are obtained by starting from a choice of vertices in $A×B$ and extending this choice to a complete subtree.