Question

You want to create an ID code for the students in your school based on three characters. The first and second characters must be a letter of the alphabet, and the third must be a digit between 1 and 9 inclusive. To find out how many different codes there are, would a list or tree diagram be practical in this case? Why or why not?

Answer 1

A list would work so much better cause u can list all the possibilities and the diagram would be no help in this case because a diagram is only going to show u certain parts when u can get all answers from a list.

Answer 2

Answer with explanation:

As we know that there are 26 letters in a alphabet and we are asked to use 9 digits in the third place.

So, the total number of such cases possible are or the total number of codes than can be created using a letter in the first two place and a digit in the third place are:

     26×26×9=6084

( Since in the first place there are a choice of  26 letters and for the second place again we have a choice of 26 letters as it is not mentioned that the repetition is not allowed and for the third place we have 9 choices)

• Hence, to represent these 6084 cases via tree diagram is too complex and difficult as it will have too many branches.

• Also, the listing of these cases could be done by computer but manually listing these cases is too tiring and time taking.