Hint: If you are counting the number of MIS that include the root.
As you said a MIS that includes the root cannot include its children and you will recurse on the grand children. So if for the
ith grandchild it has
k_i Maximum independent sets(k_i is the number of MIS for the subtree rooted at the grandchild i). Can you obtain a formula for the number of MIS for tree rooted at root?
If suppose the the subtrees rooted at the grand children of the root have k1,k2,k3,k4...,kt Maximum independent sets.(k1 for the 1st grand child and so on)
Now if you select one MIS from the k1 available for the first grand child, one from the k2 available for the second and so on,and add the root to it you get a MIS of the whole tree.
So you have k1 choices in the first one, k2 in the second one, k3 in the third. So shouldn't the total number of MIS be the product of these?
BTW you need to make sure that there is one MIS that contains the root