3. (7 points) There are 5 blue, 6 red, and 7 white bulbs. In how many ways can they be arranged into a garland (using all the bulbs) so that no two white bulbs are adjacent?
Answer: 365904

Solution: First, arrange all the blue and red bulbs in $C_{11}^{5}$ ways. In the gaps between them and at the ends, choose 7 positions and insert the white bulbs. There are $C_{12}^{7}$ ways to do this. In total, there are $C_{11}^{5} \cdot C_{12}^{7}$ ways to compose the garland from the available bulbs.