OCR MEI D1 2009 January — Question 1

Exam BoardOCR MEI
ModuleD1 (Decision Mathematics 1)
Year2009
SessionJanuary
TopicPermutations & Arrangements
TypeAssignment/allocation matching problems

1 Alfred, Ben, Charles and David meet, and some handshaking takes place.
  • Alfred shakes hands with David.
  • Ben shakes hands with Charles and David.
  • Charles shakes hands with Ben and David.
    1. Complete the bipartite graph in your answer book showing A (Alfred), B (Ben), C (Charles) and D (David), and the number of people each shakes hands with.
    2. Explain why, whatever handshaking takes place, the resulting bipartite graph cannot contain both an arc terminating at 0 and another arc terminating at 3 .
    3. Explain why, whatever number of people meet, and whatever handshaking takes place, there must always be two people who shake hands with the same number of people.