2 A small party is held in a country house. There are 10 men and 10 women, and there are 10 dances. For each dance a number of pairings, each of one man and one woman, are formed. The same pairing can appear in more than one dance. A graph is to be drawn showing who danced with whom during the evening, ignoring repetitions.

1. Name the type of graph which is appropriate.
2. What is the maximum possible number of arcs in the graph? Dashing Mr Darcy dances with every woman except Elizabeth, who will have nothing to do with him. She dances with eight different men. Prince Charming only dances with Cinderella. Cinderella only dances with Prince Charming and with Mr Darcy. The three ugly sisters only have one dance each.
3. Add arcs to the graph in your answer book to show this information.
4. What is the maximum possible number of arcs in the graph?