Suppose six men and six women need to stand in a line at the bank. Assume that all the twelve are distinct human beings.

(a) In how many ways can it be done, if there are no restrictions ?

(b) In how many ways can it be done if the men and women must alternate ? (hint: stand the men first in their places).

(c) In how many ways can it be done if all the men must stand next to each other ? (hint: consider the group of men as one big blob first).

(d) In how many ways can it be done if at least one of the first two in the line must be a woman ?

(e) Suppose A and B are two specific people (out of the twelve). In how many ways can all the people stand in a line so that A and B are not next to each other ?

(f) Suppose A, B, C, and D are four specific people (out of the twelve). In how many ways can all the people stand in a line so that either A and B are next to each other or C and D are next to each other ?