How many low level chumps can a level 3 party handle?

[An Enemy Spy]

The party is coming up on the big boss fight soon and I want it to be a tough battle. The boss is a level 5/1 Orc Druid/Ranger with a leopard companion and a horn that can summon Earth Elementals. To get into the cave where she will be making an offer to her Glabrezu master(the Glabrezu will NOT be in the fight), the party must fight through eleven Goblins, eight Orcs, and a Bugbear Fighter wielding a spiked chain. Instead of having the mooks bumrush them all at once because that would be way too many attacks to deal with, the Goblins will form a first wave followed by the Orcs once about half of them have been killed and then the Bugbear once most of the Orcs are down. Once the mooks have been killed the party can move into the cave to confront the main villain and her summoned Elementals.

The party consists of a Level 3 Fighter, a Level 3 Cleric, a Level 3 Rogue, a Level 3 unknown character(the Wizard had to drop out and the player replacing him hasn't created his character yet). They will be helped by three NPCs: A Level 3/1 Fighter/Cleric, and two Warriors who are Level 3 and 2. Is this an unfair matchup for my players?

[denthor]

I going guess 3.5 that is too much to handle for 3rd level party. You do not say what size earth elemental. But cut it in half and small elemental summons 1d4

[An Enemy Spy]

I threw a Large Earth Elemental at them last session to see if they could handle and they beat in two rounds, mainly because I forgot Elementals can't suffer critical hits that won't be an issue against orcs and goblins.

[nedz]

The strength of a party depends on these four things, in order
How well the party work together
How well each player plays their character
How strong the characters builds are
The levels of the character

We can't answer the first two, but looking at the encounter
Goblins: easy
Orcs: swingy - they can be very strong in offence even if they are easy to push over. These could end the party.
Bugbear: stronger if used as a stealth opponent, but could still shut down the parties options.

I would expect that the party should defeat these, but may not.
In any event they would need to rest up before tackling the boss.

[Calthropstu]

In theory, infinite.
This particulr scenario, they will need a choke point. A hallway will do.
Smash down the floor so the goblins can't attack. Have the party equip returning thrown weapons. Mow them down infinitely as long as they don't have ranged.

If this is a grand ballroom or something similar, the party will likely lose a member if they don't play it smart. They need to retreat and hold a choke point. Even if creating a pit is impossible, they can still reduce the attacks considerably just by making them congregate at a doorway.
It's all about tactical acumen. I could direct it into a party win, but a lot of parties would fail.

[tyckspoon]

The goblins shouldn't be much more than a speed bump. Orcs can potentially do a lot of damage, and the party doesn't have much in the way of magic access to mitigate that - bad dice here could easily see some of the party put down or at least savaged to the point they don't feel comfortable trying to push on to the final fight (ie they heal up but the Cleric is all tapped out.) ... or all the Orcs could go down in one shot without hitting anybody.

[Allanimal]

Good advice from previous posters, but I would also like to direct you to an encounter calculator. (http://www.d20srd.org/extras/d20encountercalculator/)

While CR is not an exact science, this can give you a feel for where things stand.
Of course, extreme differences in optimization on either side, how well each team works together, etc will adjust how easy or hard the encounter will be, so you need to take the results as a guideline.

[denthor]

Count the number of attacks per round

6 to start

Three down 8 more appear 11 per round

6 more down.

A large fighter shows up 6 per round.

Leopard claw claw bite all +4 to hit pounce rend

Unknown number of elementals

5th level druid (all spells used)/1 ranger that can be 2 more

Overwelming

[Karl Aegis]

Just giving your humanoids slings, javelins or crossbows would wipe out any third level party.

[Mechalich]

Large numbers of low level mooks are highly vulnerable to appropriate crowd-control spells. A single color spray or web casting, for example, can drastically re-shape this encounter. So it really matters if the party knows what they are up against and is also capable of preparing accordingly (so it really, really, matters what you replace the wizard with).

[An Enemy Spy]

UPDATE: I ran an encounter to test the three player(the new player is proving to be somewhat flaky) party's strength by having them encounter an Owlbear along with ten Goblins. The Owlbear got in some decent hits on the party, managing to do some good damage to the Rogue, Fighter, and Cleric before they brought it down with help from the NPC Fighter/Cleric. Meanwhile, the Goblins were virtually useless, managing to do little more than a few scattered points of damage and divert attention from the Owlbear. The two NPC Warriors took care of them almost by themselves while the PCs focused on the Owlbear.

My new idea is to have two Bugbear fighters each leading a group of four Orcs. One will fight the PCs outside the cave the Boss is in and the others will try to divide the party on the inside and take them on before they can get to the boss.