A committee consisting of six persons is to be selected from five women and six men.

(a) Calculate the number of ways in which the chosen committee will contain exactly two men.

(b) Given that the committee is to contain at least two men, show that it can be selected in 456 ways.

(c) Given that these 456 ways are equally likely, calculate the probability that there will be more men than women on the committee.

(d) At a meeting the members of the chosen committee sit at a rectangular table in the fixed seats illustrated in the diagram: (i) Given that each may sit in any of the six places, calculate the number of different ways they may be seated at the table.

(ii) Given that the committee consists of three men and three women and that the men and women must sit alternately round the table, calculate in how many different ways they may be seated. (L Additional)