A committee of eight members consists of one married couple together with four other men and two other women. From the committee a working party of four persons is to be formed. Find the number of different working parties which can be formed. Find also the number if the working party

(a) may not contain both the husband and his wife,

(b) must contain two men and two women,

(c) must contain at least one man and at least one woman. The eight committee members sit round an octagonal table, their positions being decided by drawing lots. Find the probability of

(d) the man sitting next to his wife,

(e) the man sitting opposite to his wife,

(f) the three women sitting together. (AEB)