Question

How can a tree diagram help you determine the number of possible ways in which selections can be made?

Answer 1

These types of problems are pretty straight forward and are very easy to solve. This particular problem is a great example of tree diagram and its application. This problem is of the topic permutations and combinations but it can also be further extended to the theory of probability, which is nothing but the number of possible outcomes upon the total number of outcomes. While choosing the number of possible outcomes, we need to determine the number of possible ways in which selections can be made. A tree diagram can be made by splitting up the problem into more and simpler sub problems.

Complete step-by-step answer:
Now we start off with the solution to our given problem by writing that, Tree diagrams generally represent or display all the possible outcomes of any event. In other words, it is basically the total number of outcomes for an event (favourable + unfavourable). Suppose there are three students, “Smith”, “Rohan” and “Adam”, there is a voting process to choose a monitor and an assistant monitor.
Case-1: Suppose Smith is elected as monitor, then Rohan and Adam will be contesting for assistant monitor.
Case-2: If Rohan is elected as monitor, then Smith and Adam will be contesting for assistant monitor.
Case-3: If Adam is elected as monitor, then Smith and Rohan will be contesting for the assistant monitor.
From the above given description we can easily draw the tree diagram. We can find the number of outcomes from Case-1 as $2$, from Case-2 as $2$ and from Case-3 as also $2$. So the total number of possible ways are $2+2+2=6$ ways.

Note: For such types of problems, we need to have a clear cut idea and an in depth understanding of permutations and combinations along with the theory of probability. We also need to be very careful while calculating the number of outcomes as each and every branch of the tree represents an outcome of an event and has to be considered separately. Tree diagrams are especially very useful in probability.