Examveda

# 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. 864

B. 863

C. 865

D. 1728

### Solution(By Examveda Team)

Required number of ways,
= 3C2 × 4! × 4!
= 1728

This Question Belongs to Arithmetic Ability >> Permutation And Combination

1. Let the 8 crew members be

{L1,L2,L3,R1,R2,E1,E2,E3}

where the 3 L's can only row on the left side, the 2 R's
can only row on the right side, and the 3 E's can row on
either side.

Since all three L's must row on the left, we only need to choose
1 of the E's to row on the left.

We can choose this E any of 3 ways.

The other 4 crew members will row on the right side.

For each of those 3 ways to choose the fourth crew member for
the left side, there are 4! ways to arrange the 4 crew members on
the left side, and 4! ways to arrange the 4 crew members on the
right side.

Answer 3*4!*4! = 3*24*24 = 1728 ways.

2. Left side arrangement:- 4P3
right side arrangement:- 4P2
and remaining 3 members arrangement on 3 seats:- 3P3
So Total ways:-4P3*4P2*3P3=1728.

3. Left side arrangement:- 4P3
right side arrangement:- 4P2
and remaining 3 members arrangement on 3 seats:- 3P3
So Total ways:-4P3*4P2*3P3=1728.

Related Questions on Permutation and Combination