Agroup of n ? 4 people stand in line to purchase movie tickets. assume that there are r ? 2 men and s ? 2 women, such that r + s = n. you should not assume that the men and women are indistinguishable from each other.
a) how many possible lines are there such that, starting from the front of the line, there are exactly three points where the line alternates from man to woman, or woman to man? for example, if n = 6, r= 4, s = 2, then one line arrangement that should be counted is (man 1, man 2, woman 1, man 3, man 4, woman 2). note that there are exactly three points of alteration- between man 2 and woman 1, woman 1 and man 3, and man 4 and woman 2
b) solve the above problem with the added condition that man 2 must be the second man in line, woman 2 must be the second woman in line, or both