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 three-person subcommittee, what fraction of all the possible subcommittees that include Cara, also include Dan? Options.
A) 1/5  B) 1/4  C) 1/3  D) 2/3  E) 2/5
The number of possible subcommittees with Cara is 6C2=15.   The number of possible subcommittees with Cara and Dan is 5C1=5.   The fraction of Cara's subcommittees which include Dan is 5/15=1/3.   The answer is 1/3.
<result>C</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 three-person subcommittee, what fraction of all the possible subcommittees that include Cara, also include Dan?