Solution 4.7.8.1.

  1. There were 24 couples: 6 choices for the girl and 4 choices for the boy.

  2. There were 45 couples: \({10 \choose 2}\) since we must choose two of the 10 people to dance together.

  3. For part (a), we are counting the number of edges in \(K_{4,6}\text{.}\) In part (b) we count the edges of \(K_{10}\text{.}\)

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