Question

7 gentlemen and 4 ladies can sit at a round table so that two particular ladies may not sit together in

• A. 7!3!2! ways
• B. 6! ${}^6{P}_4$
• C. 6! ${}^7{P}_4$
• D. 6! ${}^4{P}_2$ ways

Answer 1

Answer: (C)

6! ${}^7{P}_4$

$7$ gentlemen can be arranged around a table in $6!$ ways

$[\because$ things can be arranged around a table in $(n-1)!ways]$

Women is to be placed between $2$ men as no two women can be together.

There are $7$ gaps between men and $4$ ladies are to be placed.

This can be done in ${}^7{P}_4$ ways

$\therefore 6!{\times }^7{P}_{4}ways$ option $C$