Question

A communications company offers 16 different television packages and 16 different internet packages. Of those, 5 packages include both television and internet. How many ways are there to choose either television or internet, but not both?

Answer 1

A communication company offers 16 different television packages and 16 different internet packages. ​

The number of ways of selecting a television package is in ​ ways. And the number of ways of selecting an internet package is in ​ ways. Since there are 5 packages which includes both television and internet​ packages, there are number of ways in choosing both television and internet packages.

Given below is the inclusion–exclusion principle. We will use this to find the number of ways to choose television or internet package.

"The inclusion–exclusion principle is a counting technique which generalizes the familiar method of obtaining the number of elements in the union of two finite sets A and B; symbolically expressed as

Let T be the event (number of ways) in selecting television package and I be the event (number of ways) in selecting internet package.

Now by using the Inclusion-Exclusion Principle, the number of ways of selecting television or internet package is,

So far we have found the number of ways of choosing either television or internet package.

However, we must exclude those selections in which we select both television or internet package. Therefore, the number of ways in selecting the television or internet packages, but not both, is

Thus there are 22 number of ways to choose either television or internet package, but not both.