Teammates Four couples at a dinner party play a boardgame after the meal. They decide to play as teams of twoand to select the teams randomly. All eight people writetheir names on slips of paper. The slips are thoroughlymixed, then drawn two at a time. How likely is it thatevery person will be teamed with someone other than theperson he or she came to the party with?

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Teammates Four couples at a dinner party play a board
game after the meal. They decide to play as teams of two
and to select the teams randomly. All eight people write
their names on slips of paper. The slips are thoroughly
mixed, then drawn two at a time. How likely is it that
every person will be teamed with someone other than the
person he or she came to the party with?

Expert Solution
Total Possible Pairing

Let's call the four couples A, B, C, and D, and label the individuals in each couple with letters A1, A2, B1, B2, C1, C2, D1, and D2.

For every person, there are 6 possible partners they can be paired with. Since there are 8 people in total, there are a total of (8 choose 2) = 28 possible pairings.

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