Including Cara and Dan, there are seven members on the board of directors for a company. If the board is to be split up into a four-person subcommittee, what fraction of all the possible subcommittees that include Cara, also include Dan? Pick one:
A) 1/5
B) 1/4
C) 1/3
D) 1/2
E) 2/5
The number of possible subcommittees with Cara is 6C3=20.   The number of possible subcommittees with Cara and Dan is 5C2=10.   The fraction of Cara's subcommittees which include Dan is 10/20=1/2.   The answer is 1/2.
<result>D</result>
Including Cara and Dan, there are seven members on the board of directors for a company. If the board is to be split up into a four-person subcommittee, what fraction of all the possible subcommittees that include Cara, also include Dan?