Ms. Crosby is hiring teachers for the science department at a new high school. There are 10 biology teachers and 6 chemistry teachers to choose from. For the physics teacher, Tristan has 5 options. How many different ways can Ms. Crosby hire a staff that includes one teacher in each subject?

Question

ways

Answer 1

To determine the total number of ways Ms. Crosby can hire one teacher for each subject (biology, chemistry, and physics), we can multiply the number of options available for each subject.

1. Biology teachers: There are 10 options.
2. Chemistry teachers: There are 6 options.
3. Physics teachers: There are 5 options.

The total number of ways to hire the teachers is given by the product of the number of options for each subject:

\[ \text{Total ways} = (\text{Biology options}) \times (\text{Chemistry options}) \times (\text{Physics options}) \]

Substituting the numbers we have:

\[ \text{Total ways} = 10 \times 6 \times 5 \]

Calculating this step by step:

1. Calculate \(10 \times 6\): \[ 10 \times 6 = 60 \]

2. Now take the result and multiply by 5: \[ 60 \times 5 = 300 \]

Therefore, the total number of different ways Ms. Crosby can hire the staff is

\[ \boxed{300} \]