An n-way join performs consecutive n-1 joins among n tables. for each of the following 8-way joins, state how many join orders are possible and why (make sure to explain the reason). note ri ⋈ rj and rj ⋈ ri (switching around the order of two joined relations) are different join orders. in the join expressions below, ⋈ denotes an inner join, |⋈ denotes a left outer join, ⋈| denotes a right outer join, and |⋈| denotes a full outer join. hint: note commutativity of the different types of join operations.

a) r1 ⋈ r2 ⋈ r3 ⋈ r4 ⋈ r5 ⋈ r6 ⋈ r7 ⋈ r8

b) r1 ⋈ r2 ⋈ r3 |⋈ r4⋈ r5 ⋈ r6 ⋈ r7 ⋈ r8

c) r1 ⋈ r2 ⋈ r3 ⋈| r4⋈ r5 ⋈ r6 ⋈ r7 ⋈ r8

d) r1 ⋈ r2 ⋈ r3 |⋈| r4⋈ r5 ⋈ r6 ⋈ r7 ⋈ r8