7.1. (16 points) Vasya's parents allowed him to buy himself two toys. In the store, there are 7 different remote-controlled cars and 5 different construction sets. In how many ways can he choose his gift?
Answer: 66.

Solution. Vasya can choose one car and one constructor in $5 \cdot 7=35$ ways, two different cars in $-\frac{7 \cdot 6}{2}=21$ ways (one car can be chosen in 7 ways, one of the remaining in 6 ways, but in this way each pair of cars is counted exactly twice), and two constructors in $-\frac{5 \cdot 4}{2}=10$ ways. In total, we get $35+21+10=66$ ways.

The problem can also be solved differently: note that Vasya can buy $7+5=12$ different toys in the store, so a pair of them can be chosen $\frac{12 \cdot 11}{2}=66$ different ways.