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.

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Solution

First we arrange the three person on left side and two on right side.
Selecting $4$ people for each side can be done in $4! \times 4!$ ways
While for $3$ people we have $^{3} C_{2}$ ways
So, number of ways $^{3} C_{2} \times 4! \times 4!$
$= 1728$
Hence, the answer is $1728.$

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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.

First we arrange the three person on left side and two on right side.Selecting 4 people for each side can be done in 4!×4! waysWhile for 3 people we have 3C2 waysSo, number of ways 3C2×4!×4!=1728Hence, the answer is 1728.

First we arrange the three person on left side and two on right side.
Selecting $4$ people for each side can be done in $4! \times 4!$ ways
While for $3$ people we have $^{3} C_{2}$ ways
So, number of ways $^{3} C_{2} \times 4! \times 4!$
$= 1728$
Hence, the answer is $1728.$