Question

chemist is trying to find out how many different molecules she can make by adding a chlorine, fluorine, or bromine to an existing molecule. If there are 4 places that these elements can be added to the existing molecule, how many different molecules could the chemist make? Be sure to state if the problem involves a permutation or a combination and state if repetition is allowed. Show all of your work and explain your answer.

Answer 1

- There are 4 slots to place the molecules and we have 3 molecules.

- There can be a repetition of atoms becuase a molecule containing 1 atom of bromine is different from a molecule that contains 2 atoms of bromine, and so on.

- If we let F- Fluorine, B- Bromine, C- Chlorine,

- This problem can be classified as a Permutation problem since placing an atom F before an atom B of Bromine, is a different molecular structure from placing an atom B before an atom F.

- Thus, we can solve the question as follows:

Slot 1: We can have any of the 3 molecules fit in here.

Slot 2: We can have any of the 3 molecules fit in here and we'd still get a different molecule

Slot 3: We can also have any of the 3 molecules fit in here

Slot 4: We can also have any of the 3 molecules fit in here as well.

- Thus, the number of different molecules that can be made is

`3*3*3*3=81`