1. **Problem statement:** We need to find the number of ways to arrange 5 boys and 6 girls in a line such that all 5 boys occupy 5 consecutive positions. 2. **Understanding the problem:** We have 11 people total (5 boys + 6 girls). The 5 boys must be together as a block. 3. **Step 1: Treat the 5 boys as a single block.** - This block plus the 6 girls means we have $6 + 1 = 7$ entities to arrange. 4. **Step 2: Arrange the 7 entities.** - The number of ways to arrange these 7 entities is $7!$. 5. **Step 3: Arrange the boys within their block.** - The 5 boys can be arranged among themselves in $5!$ ways. 6. **Step 4: Calculate total arrangements.** - Total ways = ways to arrange 7 entities $\times$ ways to arrange boys inside the block - $$7! \times 5!$$ 7. **Step 5: Calculate the numerical value.** - $7! = 5040$ - $5! = 120$ - Total ways = $5040 \times 120 = 604800$ **Final answer:** There are $604800$ ways to arrange 5 boys and 6 girls so that the boys occupy 5 consecutive positions.