One evening, Mr and Mrs Smith invite Mr and Mrs Andrews, Mr and Mrs Brown, Mr and Mrs Churchland and Mr and Mrs Steele around for dinner. As everyone arrives people shook hands, and Mr Smith observed the following facts:

• No pair shook hands more than once.
• No one shook their own hand.
• No one shook their spouse's hand.

After the dinner, Mr Smith asked everyone else how many times they had shaken hands this evening. He discovered that they had all done it a different number of times.

How many people did Mrs Smith shake hands with?