In each of the following three cases, find all possible $$structurally$$ different

B$-$tree indexes of order n $=3.$

$($a$).$ For a data file with $6$ records.

$($b$).$ For a data file with $10$ records.

$($c$).$ For a data file with $15$ records.

Hint: First find possible structures of interior and leaf nodes for n $=3.$