You should be able to run them together, the only problem is they may cause everything to run in single channel mode. Hard to say with out RAM/MOBO specs, Make/Model. They would normally be added to the remaining slots. If you have a MOBO manual, it should give details about how to load the RAM and what configs are supported. I did have one MOBO that would not support SS with DS RAM.
Suppose you have 6 slots of RAM. If you use 1 stick of RAM in a single slot out of those 6 it's going to be Single Channel.
If you use 2 Slots each with 1 single Module of RAM in it, it's going to work as DUAL Channel and if you use 3 Sticks of RAM in three of those slots they work as Tri Channel RAM.
In the stores, you get Dual Channel and Tri Channel Kits of RAM. That is , so that you don't get BSODs when you try to create a tri channel set by yourself, mixing up RAMs of different batches. It just cuts down the possibility of having a mismatch somewhere.
It is always better to go by buying RAMs in sets of the same specs instead of mixing and matching them. These days you need to have the same size,timings and voltages to equate if you want the rig to work perfectly. And RAMs keep changing by the day, most models are stopped at the production level within 6 months of manufacture, so it's something that you need to be very particular about, as more and more boards are getting more and more sensitive to the kind of RAM that you put into them.
Suppose you have 6 slots of RAM. [...] if you use 3 Sticks of RAM in three of those slots they work as Tri Channel RAM.
Not unless you're using an X58 motherboard. The vast majority of boards are only dual channel, with the only exception being those built on Intel's X58 chipset back in 2010 (triple channel) and Intel's X79 chipset now (quad channel). Putting three sticks in any other board will not make it work in triple channel mode. Instead, you still be operating in dual channel, with one of the channels having more available memory. You'd probably be unstable as well. Multi-channel memory is very sensitive to proper pairing, who knows what mixing paired and unpaired would do.
A more accurate description would be this. Your motherboard will have some number of slots, divided up into some number of channels. These will be color coded, with no two slots of the same color being on the same channel. So, if you've got six slots, three red and three black, you've got triple channel memory (N slots of any one color means N channel memory). When you buy a triple channel kit, you'd put each of the modules in the same color slots, so each is sitting in its own channel and can be used simultaneously.
More commonly, you'd see something like six slots with three colors, each color having two slots. So you'd get two red, two black and two blue slots. This is a dual channel configuration, and nothing you do is going to make it triple channel.