Question

The number of ways in which $7$ men and $4$ women are to be seated at a round table so that no two women are to sit together is:

• A. $6!{}^7{P}_4$
• B. $7!{}^7{P}_4$
• C. $6!{}^8{P}_4$
• D. $7{}^7{P}_4$

Answer 1

Answer: (A)

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

First arrange 7 men at the round table in $6!$ ways and then
make women sit on the 7 space generated between the men which can be done in ${}^7{P}_4$ ways
Hence total number of ways is $=6!{\cdot }^7{P}_4$