Question

If in a railway carriage $5$ persons can sit each side then number of ways in which a party of $4$ girls and $6$ boys can seat themselves so that the girls will always occupy the corner seats is

• A. $17,430$
• B. $17,431$
• C. $17,280$
• D. $17,281$

Answer 1

The correct option is C $17,280$

Since the girls should be seated in corner seat always
$\therefore$ girls can be arranged in${}^4{P}_4$ ways
While boys can be arranged in the remaining seats in${}^6{P}_6$ ways.
Total ways $={}^4{P}_4\times {}^6{P}_6=17280$