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QUESTION

# A group of 7 women and 6 men comes together for a committee meeting.They will sit around a table with 14 chairs.

A group of 7 women and 6 men comes together for a committee meeting.They will sit around a table with 14 chairs.(a) If we ignore the extra chair, how many different seating arrangements are there for this group?(b) If we take the extra chair into consideration, how many different seating arrangements are there for this group?(c) It turns out that the men and women will start arguing if they are too mixed up at the table. So it is decided that along one side of the table,there will be 7 chairs - the first 3 of which will seat women, and the last 4 of which will seat men. How many seating arrangements are there on this side of the table?(d) The men decide that they need to have a subcommittee of only men to discuss this seating nonsense, and this subcommittee should have 3 people.How many different subcommittees can be formed from the men?(e) The women decide that if the men are going to have a subcommittee,then the women should also have one to discuss how silly men are. The women’s subcommittee will have 4 people. And, they decide they will give their committee a name, using the first initial of the name of each woman on the subcommittee. The first initials of the 7 women available are B,C,D,J,M,N,S. How many different names for a 4-person subcommittee can be made?