Question

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

help me!

Answer 2

The arrangement around the table must be of the form BGBGBGBG. We can place the first boy anywhere; we then have $3! = 6$ ways of placing the remaining boys and $4! = 24$ ways of placing the girls. This gives a total of $6\cdot 24 = \boxed{144}$ arrangements