Question

$5$ boys & $4$ girls sit in a straight line. Find the number of ways in which they can be seated if $2$ girls are together & the other $2$ are also together but separated from the first $2$.

• A. $43200$
• B. $28800$
• C. $21600$
• D. $10800$

Answer 1

The correct option is A $43200$

Step 1: Arrange $5$ boys in $5!$ ways
Step 2nd : Select $2$ gaps from $6$ gaps for $4$ girls ($2$ girls for each gap) in ${}^6{C}_2$ ways.
Step 3rd : Select $2$ girls to sit in one of the gaps and other $2$ in remaining selected gaps = ${}^4{C}_2$ ways
Step 4 : Arrange 1st, $2$ girls in $2!$ and other 2 in $2!$ ways.
Hence, total ways $=5!\times {}^6{C}_2\times {}^4{C}_2\times 2\times 2=43200$