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Desmond lives in Melbourne and is taking a trip to Sydney. He can travel to Sydney and back in


different ways: by bus, cab, or train. Desmond chooses how to get to Sydney and back at random.
Which of these tree diagrams can be used to find all of the different ways that Desmond can get to Sydney and back?
Choose all answers that apply:
Choose all answers that apply:
(Choice A) Diagram A
A
Diagram A
(Choice B) Diagram B
B
Diagram B


Diagram A:
A tree diagram. The starting point branches to nodes B and B. Nodes B and B each branch to a pair of C and C nodes. The four C and C nodes each branch into T and T end nodes.














Diagram B:
A tree diagram. The starting point branches to nodes B, C, and T. Nodes B, C, and T each branch to a B, C, and T ending nodes.













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1 answer

To determine which tree diagrams can be used to illustrate all the different ways Desmond can travel to Sydney and back (by bus, cab, or train), we need to analyze each diagram.

  1. Diagram A:

    • Starts with a single node.
    • This node branches into two B nodes, each of which then branches to two C nodes, and finally each C node branches to T end nodes.
    • From the description, it seems Diagram A does not adequately represent the choices Desmond can make, as it only includes buses (B) and cabs (C), but not a distinct representation for each travel method for both the outbound and inbound trips.

  2. Diagram B:

    • Starts with a single node that branches into three options: B (bus), C (cab), and T (train).
    • Each of these (B, C, T) branches again into B, C, and T, representing the choice of returning from Sydney with the same transportation methods.
    • This properly represents all combinations of going to Sydney and returning, as it covers every possibility: (B to B, B to C, B to T, C to B, C to C, C to T, T to B, T to C, T to T).

Given these analyses:

  • Diagram A does not accurately represent all the ways Desmond can travel to Sydney and back.
  • Diagram B accurately represents all the options.

Therefore, the applicable choice is:

  • (Choice B) Diagram B.