In how many different ways can 4 ladies and 4 gentlemen be seated at a round table so that all ladies sit together?  Choose the correct answer:
A) 70
B) 288
C) 576
D) 10,080
E) 20,160
Glue the ladies together so that they create one unit, so we would have 5 units: {M1}, {M2}, {M3}, {M4}, and {W1,W2,W3,W4} --&gt; # of different arrangements of nn objects around the table (circular arrangements) is (n−1)!(n−1)!, so our 5 objects can be arranged in (5−1)!=4!(5−1)!=4! ways.   On the other hand 4 women within their unit also can be arranged in 4! ways --&gt; total 4!∗4!=5764!∗4!=576.   Answer: 576.
<result>C</result>
In how many different ways can 4 ladies and 4 gentlemen be seated at a round table so that all ladies sit together?