Official Solution:Nine family members: 5 grandchildren (3 brothers and 2 sisters) and their 4 grandparents are to be seated around a circular table. How many different seating arrangements are possible so that 2 sisters are seated between any two of the three brothers?
A. 120
B. 480
C. 1440
D. 2880
E. 8640
Consider two brothers and two sisters between them as one unit: {BSSB}.
So, now we have 6 units: {G}, {G}, {G}, {G}, {B}, and {BSSB}.
These 6 units can be arranged around a circular table in \((6-1)!=5!\) ways.
Next, analyze {BSSB} unit:
We can choose 2 brothers out of 3 for the unit in \(C^2_3=3\) ways;
These brothers, within the unit, can be arranged in 2! ways: \(\{B_1, S, S, B_2\}\) or \(\{B_2, S, S, B_1\}\).
The sisters, within the unit, also can be arranged in 2! ways: \(\{B, S_1, S_2, B\}\) or \(\{B, S_2, S_1, B\}\).
Therefore, the final answer is 5!*3*2*2=1440.
Answer: C
_________________