1. **Problem statement:** (i) Find the number of different seating arrangements of eight friends sitting together in a row. (ii) Given five boys and three girls, find the number of seating arrangements where the three girls sit together. 2. **Formula and rules:** - The number of ways to arrange $n$ distinct people in a row is $n!$. - When a group must sit together, treat that group as a single unit, then multiply by the arrangements within the group. 3. **Step (i):** - Total friends: 8 - Number of arrangements: $$8! = 40320$$ 4. **Step (ii):** - Treat the 3 girls as one unit plus 5 boys, total units: $5 + 1 = 6$ - Number of ways to arrange these 6 units: $$6! = 720$$ - Number of ways to arrange the 3 girls within their unit: $$3! = 6$$ - Total arrangements with girls together: $$6! \times 3! = 720 \times 6 = 4320$$ **Final answers:** (i) $40320$ (ii) $4320$