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  4. The number of ways in which 5 girls and 3 boys can be seated in a row so that no two boys are together is

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Q. The number of ways in which $5$ girls and $3$ boys can be seated in a row so that no two boys are together is

Solution:

$5$ girls are arranged in $51$ ways where as in $6$ Gaps $3$ boys can be arranged in ${ }^{6} p_{3}$ ways.
$\therefore $ Number of ways $=5 !^{6} p_{3}=14400$