Andrew chooses a number from 1 to 100, and Mary also chooses a number from 1 to 100. (They may choose the same number.) It turns out that the product of their numbers is a multiple of 5. In how many ways could Andrew and Mary have chosen their numbers?
+2668 There are 3 cases:
Mary gets a multiple of 5 but Andrew doesn't: 20 ways for Mary to get a multiple of 5, 80 ways for Andrew to get a number that isn't a multiple of 5
So, there are \(20 \times 80 = 1600\) ways to do this.
Andrew gets a multiple of 5 but Mary doesn't: 20 ways for Andrew to get a multiple of 5, 80 ways for Mary to get a number that isn't a multiple of 5
So, there are \(20 \times 80 = 1600\) ways to do this.
Both get a multiple of 5: There are 20 ways for Andrew to get a multiple of 5, 20 ways for Mary to get a multiple of 5
So, there are \(20 \times 20 = 400\) ways to do this.
Thus, there are \(1600+400+1600 = \text{____}\) ways.
