Question

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

• A. 14040
• B. 14440
• C. 14000
• D. 14400

Answer 1

The correct option is D 14400

The arrangement can be as follows:
$\_\_G\_\_G\_\_G\_\_G\_\_G\_\_$
5 girls can be seated in five places in $5!=120$ ways.
3 boys can be seated in six blank places in ${}^6{P}_3=6\times 5\times 4=120$ ways.
$\therefore$ Total number of ways $=120\times 120=14400$