(a) In how many ways can one totally order the partial order of positive-integer divisors of 96?
(b) How many of the total orders in part (a) start with 96 > 32?
(c) How many of the total orders in part (a) end with 3 > 1?
(d) How many of the total orders in part (a) start with 96 > 32 and end with 3 > 1?
(e) How many of the total orders in part (a) start with 96 > 48 > 32 > 16?