There are 5 historical momuments, 6 gardens and 7 shopping malls in the city. In how many ways
a tourist can visit the city, if he visits at least one shopping mall?
To find the number of ways a tourist can visit the city while also visiting at least one shopping mall, we will use the principle of inclusion-exclusion.
First, we find the total number of ways to visit the city, regardless of visiting shopping malls. This can be calculated as the product of the number of options for each category: 5 historical monuments * 6 gardens * 7 shopping malls = 210.
Next, we subtract the number of ways to visit the city without visiting any shopping malls. Since the tourist must visit at least one shopping mall, there are 4 options for the tourist to choose from for the shopping mall category, as they cannot choose "no shopping mall." Thus, the number of ways to visit without visiting any shopping malls is 5 historical monuments * 6 gardens * 1 shopping mall = 30.
Using the principle of inclusion-exclusion, the number of ways to visit the city with at least one shopping mall is 210 - 30 = 180.
Therefore, the tourist can visit the city in 180 different ways while also visiting at least one shopping mall.