Question

Out of eight crew members, three particular members can sit only on the left side. Another two particular members can sit only on the right side. Find the number of ways in which the crew can be arranged so that four men can sit on each side.

• A. 865
• B. 864
• C. 863
• D. 1728

Hint:

In arrangement problems with restrictions, first consider the fixed positions and then arrange the remaining items freely.

Answer 1

The Correct Option is D

- Out of the 8 crew members, 3 particular members can sit only on the left side. So, they must be arranged in \( 4P3 \) ways on the left side.
- Another 2 particular members can sit only on the right side. So, they must be arranged in \( 4P2 \) ways on the right side.
For the remaining 3 crew members, we have 3 positions left on each side. These 3 remaining members can be arranged in the following ways:
- 3 members can be arranged in \( 3! \) ways on the left side.
- The remaining 3 members can be arranged in \( 3! \) ways on the right side.
Thus, the total number of arrangements is: \[ 4P3 \times 4P2 \times 3! = 1728 \]
Thus, the correct answer is 1728.