Question

$5$ boys & $3$ girls are sitting in a row of $8$ seats. Number of ways in which they can be seated so that not all the girls sit side by side, is?

• A. $36000$
• B. $9080$
• C. $3960$
• D. $11600$

Answer 1

The correct option is A $36000$

Total no of ways they can be arranged is without any restrictions = $8!$ ways.

No of ways in which they can be seated so that all the girls sit together = $6!\times 3!$ as the girls are treated as a singles block and they can be arrange among themselves in $3!$ ways.

No of ways in which they can be seated so that not all girls sit together = $8!-6!\times 3!=40320-4320=36000$