The items $A,B,C,D,E,$ and $F$ are to be divided between Alice and Bob by taking turns. Suppose that Alice's preference list has the items in alphabetical order and that Bob's preference list has the items in reverse alphabetical order.

$($a$)$ Determine which items Alice and Bob get if Alice chooses first and they use the top$-$down method to allocate the items. Also, determine the order of the items that Alice and Bob receive.

Alice's first choice

E

A

C

Bob's first choice

B

D

F

Bob's last choice

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