Question

a security systems contractor has the contract for installing the security system at a large warehouse. the company that owns the warehouse has a choice of 5 network hub and wiring layout, 2 different camera recording systems, 4 alarm systems, and 3 different pricing schedules. in how many different ways can the owner of the warehouse choose to install a security system? (enter your answer in the box below, without using comma in the number. the program will insert comma in the number where needed when you submit your answer). question 8 3 pts an animal rescue house has 6 cats and 13 dogs. alex shows up at the rescue house and he wants to adopt a cat and a dog. how many ways can alex pick a cat and a dog to go home with him? (enter your answer in the box below).

Explanation:

Step1: Use the multiplication principle

The multiplication principle states that if there are \(m\) ways to do one thing and \(n\) ways to do another thing, then there are \(m\times n\) ways to do both things.

For the first problem:
The number of ways to choose a network hub and wiring layout is \(5\) ways.
The number of ways to choose a camera recording system is \(2\) ways.
The number of ways to choose an alarm system is \(4\) ways.
The number of ways to choose a pricing schedule is \(3\) ways.
By the multiplication principle, the total number of ways to choose the security - system is \(5\times2\times4\times3\).

$$5\times2\times4\times3=(5\times2)\times(4\times3)=10\times12 = 120$$

For the second problem:
The number of ways to choose a cat is \(6\) ways.
The number of ways to choose a dog is \(13\) ways.
By the multiplication principle, the total number of ways to choose a cat and a dog is \(6\times13\).

$$6\times13 = 78$$

Answer:

120
78