Question

In how many ways can 3 ladies and 4 gentleman arrange themselves about a round table so that all women sit together?

• A. $120$
• B. $720$
• C. $24$
• D. $144$

Answer 1

The correct option is D $144$

Case i : All women sit together.

Women can be arranged in $3!=6$ ways. Now consider all women as a man. So we now have $5$ men . These $5$ men can arranged in round table in $(5-1)!=4!=24$ ways.

Therefore total number of ways is equal to $24\times 6=144$ ways .