A child is playing with four colored blocks: red, yellow, green, and blue. She lines up the blocks horizontally on the floor. In how many ways can she arrange the blocks so that the green and blue blocks are never directly next to each other?
Answer (1)
1. Total arrangements without restriction: There are 4 blocks (R, Y, G, B), so total arrangements = 4! = 24.2. Arrangements where G and B are together: Treat G and B as a single block → 3 items (R, Y, G-B) → 3! = 6 arrangements. Since G and B can switch positions inside the block → 6 × 2 = 12.3. Arrangements where G and B are not together: Total arrangements − arrangements where G and B are together = 24 − 12 = 12.So, there are 12 ways to arrange the blocks so that the green and blue blocks are never directly next to each other.
