There are 5 historical monuments, 6 gardens, and 7 shopping malls in a city. In how many ways a tourist can visit the city if he visits at least one shopping mall.

Answer

`2^(5)xx2^(6)xx(2^(7)-1)`

Explanation

For each historical monument there are two possibilities, either he visits or does not visit.
The number of ways in which he can visit 5 historical monuments is `2^(5)`. Similarly, he can visit 6 gardens in `2^(6)` ways.
To visit at least one of seven shopping malls, it could be in `2^(7)-1` ways.
Therefore, the total number of ways he can visit the city is `2^(5)xx2^(6)xx(2^(7)-1)`.