Anthony and David sit on the 6-member board of directors for company L. If the board is to be split up into two 3-person subcommittees, what is the percentage that David and Anthony are included in the same sub-committee?


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Answer:

40%

Step by Step Explanation:
  1. David will be on one of the two committees for sure which will leave 2 seats on that 3-member sub-committee.
  2. Now for David and Anthony to be included in the same sub-committee, Anthony has to fill one of those 2 seats of the sub-committee in which David is included.
  3. Therefore the likelihood that Anthony gets one of the remaining 2 seats =  
    Number of vacant seats in the sub-committee that includes David
    Total number of seats remaining
      =  
    2
    5
     
  4. The percentage of all the possible subcommittees that include both David and Anthony =  
    2
    5
      × 100 = 40%

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