1. **Problem statement:** We need to find the number of ways to arrange an eight-oared boat crew from 11 men. Among them, 3 can steer but cannot row, and the rest cannot steer. Additionally, 2 men can only row on the bow side. 2. **Understanding the problem:** - The boat has 8 rowers. - 3 men can steer but cannot row, so they cannot be part of the 8 rowers. - The remaining 8 men (11 - 3 = 8) can row. - Among these 8 rowers, 2 can only row on the bow side. 3. **Crew composition:** - Since 3 men cannot row, the 8 rowers must be chosen from the 8 men who can row. - The 8 rowers must be arranged with 4 on the bow side and 4 on the stroke side. 4. **Constraints:** - 2 men can only row on the bow side. - The other 6 men can row on either side. 5. **Step 1: Assign bow side rowers:** - Bow side has 4 positions. - 2 men must be on bow side (since they can only row there). - We need to choose the remaining 2 bow side rowers from the 6 men who can row on either side. - Number of ways to choose these 2 bow side rowers: $\binom{6}{2}$. 6. **Step 2: Assign stroke side rowers:** - Stroke side has 4 positions. - Stroke side rowers must be chosen from the remaining 4 men (6 - 2 chosen for bow side = 4). - Number of ways to choose stroke side rowers: $\binom{4}{4} = 1$. 7. **Step 3: Arrange rowers on each side:** - The 4 bow side rowers can be arranged in $4!$ ways. - The 4 stroke side rowers can be arranged in $4!$ ways. 8. **Step 4: Calculate total number of arrangements:** $$\binom{6}{2} \times \binom{4}{4} \times 4! \times 4! = 15 \times 1 \times 24 \times 24 = 8640$$ **Final answer:** There are $8640$ ways to arrange the crew under the given conditions.