The most common raid setups are 2 melee, 1 caster, 1 BRD. This is because of a few main reasons:
1) MP usage is a common problem for healers in FCoB, making the BRD very useful for sustain.
2) TP usage for melee DPS is sky high in FCoB due to the fights having very little down time. This again makes BRD very useful.
3) Caster LB is very helpful in a couple of the turns, making one caster helpful.
4) The cube in T11 is resistant to physical DPS, making one caster helpful here.
5) FCoB fights tend to be very melee friendly in their mechanics, making a second melee DPS helpful.
6) More than 2 melee can make the area around the boss very crowded, increasing the difficulty in some fights.

My raid follows this logic:
DRG, MNK, BRD, BLM
This is because:
1) DRG is great with any party that has a BRD
2) High MNK dps as well as dragon kick for the int debuff
3) BLM is currently significantly better than SMN by a decent margin, making it preferable
4) BRD helps a lot for TP and MP regen

Trading out a DRG for a NIN is very common due to the solid utility and similar DPS output they bring. Also, trading out BLM for SMN can be done without much trouble, though they require a bit more skill to play and really lack in the burst AoE department. Dropping the MNK requires that parties have a bit more HP since they will not have access to the 10% intelligence debuff.

All that being said, there are some groups who have great success with different compositions, though those comps require more skill from the group and allow less room for errors. All of FCoB is completable with other comps than the 2 melee, 1 caster, 1 BRD, but they tend to be less optimal overall.