Ben and Shari have invited three other couples to their apartment for a game of charades. Everyone is to be split into two equal teams, but each team must consist of either two couples or no couples. How many different pairs of teams are possible? Answers: A) 11 B) 14 C) 22 D) 35 E) 70
Ben and Shari can be paired with any of the other three couples, leaving the remaining two for the other team. So, the number of ways to split 4 couples into two teams is 3:   {1, 2} - {3, 4}   {1, 3} - {2, 4}   {1, 4} - {2, 3}   The number of teams where there are no couples:   {Ben, any from couple 2, any from couple 3, any from couple 4} and the remaining 4 people form team #2. The number of team for Ben = 2*2*2= 
<gadget id="calculator">2*2*2</gadget>
<output>8</output>
8.   Total= 3 + 8= 
<gadget id="calculator">3 + 8</gadget>
<output>11</output>
11.   11nswer: 11
<result>A</result>
Ben and Shari have invited three other couples to their apartment for a game of charades. Everyone is to be split into two equal teams, but each team must consist of either two couples or no couples. How many different pairs of teams are possible?