Question

at a local hardware store, adam is selecting tools for a small toolkit, which will include one of each type of tool. there are 5 hammers and 6 screwdrivers to choose from. for the wrench, adam has 8 options. lastly, there are 4 possibilities for the saw. how many different toolkits can adam build?

□ toolkits

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Explanation:

Step1: Identify the multiplication principle

To find the total number of different toolkits, we use the multiplication principle of counting, which states that if there are \( n_1 \) ways to do one thing, \( n_2 \) ways to do a second thing, \( n_3 \) ways to do a third thing, and \( n_4 \) ways to do a fourth thing, then the total number of ways to do all four things together is \( n_1\times n_2\times n_3\times n_4 \). Here, the number of choices for hammers is \( n_1 = 5 \), for screwdrivers is \( n_2=6 \), for wrenches is \( n_3 = 8 \), and for saws is \( n_4=4 \).

Step2: Calculate the total number of toolkits

We multiply the number of options for each type of tool:
\[
5\times6\times8\times4
\]
First, calculate \( 5\times6 = 30 \). Then, \( 30\times8=240 \). Finally, \( 240\times4 = 960 \).

Answer:

960