Question

There are 25 employees in an office. 18 have cell phones, 11 have cars, and 8 have both. How many of them don't have anything

Answer 1

To determine how many employees don't have either a cell phone or a car, we used the principle of inclusion-exclusion: 21 employees have either one or both. Subtracting this from the total of 25 employees, we find that 4 employees don't have either.

Step-by-step explanation:

To determine the number of employees who don't have a cell phone or a car, we can use the principle of inclusion-exclusion. First, let's add the total number of employees who have either a cell phone or a car, then subtract the ones who have both to avoid double-counting.

The formula for the principle of inclusion-exclusion is:

Total = Number with Cell Phones + Number with Cars - Number with Both

Now, plug in the numbers:

Total = 18 + 11 - 8 = 21

So, there are 21 employees who have either a cell phone, a car, or both. To find out how many don't have either, subtract this number from the total number of employees:

Employees without Both = Total Employees - Total with Either

Employees without Both = 25 - 21 = 4

Therefore, 4 employees don't have either a cell phone or a car.

Answer 2

By applying the principle of inclusion-exclusion, it is determined that 4 employees in the office don't have either a cell phone or a car.

Step-by-step explanation:

To determine how many employees in the office don't have either a cell phone or a car, we can use the principle of inclusion-exclusion in set theory. Here's how it's applied to this problem:

• Total number of employees = 25
• Employees with cell phones = 18
• Employees with cars = 11
• Employees with both cell phones and cars = 8

We calculate the number of employees with at least one of the two items (either a cell phone or a car) by adding those with cell phones to those with cars and then subtracting those who have both:

Employees with at least one item = Employees with cell phones + Employees with cars - Employees with both

= 18 + 11 - 8

= 29 - 8

= 21

We then subtract the number of employees with at least one item from the total number of employees to find out how many don't have anything:

Employees with neither = Total number of employees - Employees with at least one item

= 25 - 21

= 4

Therefore, 4 employees in the office don't have either a cell phone or a car.