So, to prove that a well-chosen multiclass group is easier to gear than a 4shaman+paladin group, this is a set of calculations that check how much chance there is to get a useful drop for an item for the first drop.

Considerations:
Here are some reasonable assumptions to make the calculations easier. Feel free to comment for corrections.

1) Drops in heroics drop this kind of gear:
- tanking plate(has def/dodge/etc)
- tanking leather(has def/dodge)
- pure melee leather (AP-related)
- pure melee mail (AP-related)
- pure melee plate (AP-related)
- melee leather with int (has AP-related stats with int)
- melee mail with int (has AP-related stats with int)
- melee plate with int (has AP-related stats with int)
- cast cloth
- cast leather
- cast mail
- cast plate
We assume that cast gear is useful for both DPS and healing.
Total: 12 types of gear.
2) When an item drops (world drop and boss drop), any item category has equally much chance to drop. So when an item drops there's 8.33% chance (1/12) that it belongs to ANY specific category.
3) Each class is assumed to have 1 specific role and we assume that healing gear can also be used for cast dps gear and vice versa.

Calculations:
1) 4 shamans + 1 paladin tank:
- Shamans can wear cloth, mail and leather, which covers 3 gear types out of the 12 that drop.
- This leads to the chance P for shaman gear: P(shamangear) = 3/12 = 0.25 (25%)
- A paladin tank is assumed to wear plate with defense stats, so his gear only is covered by 1 gear type out of 12
- This leads to the chance P for paladin gear: P(paladingear) = 1/12 = 0.08333 (8.3%)
- shamangear and paladingear don't share elements, so mathematically this becomes: P(shamangear or paladingear) = P(shamangear) + P(paladingear) = 0.3333% =~ 33%
Conclusion: The first item that drops for a 1paladin-4shaman group has 33% chance to be of use to that group.

2) 1 paladin healer, 1 hunter, 1 mage, 1shaman and 1 druid tank:
Since some classes share gear, I will list the useable gear first:
- pure melee leather (AP-related) -> useable for hunter
- pure melee mail (AP-related) -> useable for hunter
- melee leather with int (has AP-related stats with int) -> useable for hunter
- melee mail with int (has AP-related stats with int) -> useable for hunter
- tanking leather
- cast cloth -> useable for mage/shaman/paladin
- cast leather -> useable for mage/shaman/paladin
- cast mail -> useable for mage/shaman/paladin
- cast plate -> paladin
This totals 9 usable gear drops.
So the chance of a useful drop becomes 9/12 = 75% chance to get a useful item on the first drop.

Conclusion:
The first item drop for a 4shaman+1paladin team has a 33% chance of being useful, while the first item drop for the mixed group has 75% of being useful.

Appendix:
On following drops, the calculation becomes a lot more complex, because you have to consider for each class that the gear slot might be taken and you have to consider how many classes that can use the newly dropped gear.
For the shamans this means that consecutive cast gear drops are useful right until the 4th drop of any specific slot-related drop.
For the multiclass group this becomes a lot more complex to calculate.

I'll add more calculations later in relation to consecutive drops.

[edit] Multiclass listing