2. (5 points) On Valentine's Day, every student in the school gave each female student a valentine. It turned out that the number of valentines was 42 more than the total number of students. How many valentines were given?
Answer: 88

Solution: Let $x, y$ be the number of boys and girls in the school, respectively. According to the problem, $x y = x + y + 42$. Then $(x-1)(y-1) = 43$. Therefore, the numbers $x-1$ and $y-1$ are 1 and 43. The number of valentines is $2 \cdot 44 = 88$.

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(using all the bulbs) a garland can be formed so that no two white bulbs are adjacent.

Answer: 910910

Solution: First, arrange all the blue and red bulbs in $C_{14}^{5}$ ways. In the gaps between them and at the ends, choose 12 positions and insert the white bulbs. There are $C_{15}^{12}$ ways to do this. In total, there are $C_{14}^{5} \cdot C_{15}^{12}$ ways to form a garland from the available bulbs.