Let us denote girls as G1, G2, and G3
And boys as B1, B2, and B3
Let us first make the girls sit together (ladies first indeed).
G1,G2,G3
G2,G1,G3
..............
..............
(total 3! = 6 permutations)
Now, let us make gaps in both sides of the girls ...
_G1_G2_G3_
So, a total of 4 gaps are there where boys are to be inserted.
B1 G1 B2 G2 B3 G3
B2 G1 B1 G2 B3 G3
.............................
.............................
(Total 4P3 = 24 permutations for this setting of girls)
Therefore, total 24*6 = 144 different arrangements are possible ...
Let me know if I am wrong:hmm: