Quandaries and Queries


Name: Denean

Who is asking: Parent Level: Elementary


  1. For lunch, students can choose juice or milk; hamburger or pizza; and a banana or apple. How many lunch combinations can the students make?

  2. In an experiment, Monty can use paper towels or cloth. He can choose red, green, or yellow food coloring. How many combinations are there?


Hi Denean,

A tree diagram is a big help in approaching this type of problem. For the first problem there are three courses to lunch, a drink, a main course and a desert. My tree is thus going to have three levels, one for each course, in the order drink, main course and then desert. You can choose any order you wish.

Starting at the bottom of the tree there are two choices at the first level, juice or milk. Thus there are two branches at this level to choose from. I labeled them J for juice and M for milk. Once you have a drink, you have two choices for a main course and hence there are two branches here also, one labeled H for hamburger and the other P for pizza. Likewise at the third level. My tree diagram is below.

Choosing a lunch is then climbing from the bottom of the tree to the top and collecting an item on each branch. There are eight nodes at the top of the tree and hence eight ways to climb up the tree. Each gives a different lunch combination.

Now try the second problem. Here there are only two levels in the tree, one for a material and the other for a colour. The colour level has three choices however, so there will be three branches to choose from at this level.


Go to Math Central