In how many ways can 4 boys and 4 girls sit around a circle table if all the boys sit together? (Rotations of the same arrangement are still considered the same. Each boy and girl is unique, not interchangeable.)

Answer 1

Visualize them all in a row.
The four boys can be arranged in 4x3x2x1
and then the girls can be arranged in 4x3x2x1 ways
which is 24x24 or 576 ways
Now if we seat them there are 8 possible rotations without changing the order, so

number of ways to seat them is 576/2 or 288 ways

Answer 2

Incorrect, It is 144