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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

Answer: Option D

Solution(By Examveda Team)

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

This Question Belongs to Arithmetic Ability >> Permutation And Combination

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Comments ( 3 )

  1. Orko Abir
    Orko Abir :
    4 years ago

    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. Kumar Chandan
    Kumar Chandan :
    9 years ago

    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. Kumar Chandan
    Kumar Chandan :
    9 years ago

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

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