EMT Conduit Capacity with Mixed Gauge
Solid vs stranded

A lot of people who work 99% in Romex find themselves gravitating toward solid wire because "it's the devil they know", they have no idea the difference, and they fret about terminations. 

I work 99% in conduit and stranded is the only way to go.  When you have a solid wire in the bundle (I'm cheap, I reuse wire). you know it and it's a fighter.  As far as terminations, they're a little more finicky sometimes, but it's not a big deal.  If one is out of your comfort zone,  pigtail a bit of solid wire (wire nut splices solid-stranded are just fine).   You want to be in stranded.  Seriously.

#10 is the breakover above which all wire must be stranded.  As such, #10 solid is a black swan - nobody who does conduit for a living wants to pull it, and so it is relegated to a specialty item.  What's more, every termination meant to take #10 (eg NEMA x-30 receptacles) is designed for stranded wire. 

We generally advise  people to underfill conduit to keep the effort of pulling easy.  That's why we'd tell you to use 2" conduit for three #2’s.  Otherwise you could run out of swear words and have to call the guy with a truck full of pulling tools, and he probably won't want to come in for just the pull.  Since you are near conduit fill limits, you should expect a challenging pull.  If you attempt this with solid wire, you should expect a very, very challenging pull.

You may be tempted to dismantle the conduit and reassemble it around the pulled wire.  That is not allowed, and will work particularly badly with solid wire. 

Conduit fill

RME describes the gory details and the source material.  I just google "conduit fill calculator" and pick one I like.  One that lets me state # of wires of each size, and does the lookups for me.  

For conduit fill (NOT derate), neutrals and grounds count, as do for instance fiber optic lines or Class II wiring, since they all take space.  

Solid vs stranded doesn't matter, the slightly larger size of stranded is a "gimme".  There are a lot of gimme's in fill calcs, wait til you get into junction boxes!  

You're fine, but you are also essentially full. 

Conduit wire derate

This won't affect you because you are full. 

Too many wires in one conduit will get too hot (you're a long way from this problem).  In residential/split phase, each circuit can only have 2 conductors because like I said, neutrals and grounds don't count.  But even if you were doing something odd (lopsided hot/neutral on 3rd circuit? Two 3-phase delta circuits?) it matters not: 4-6 wires have the same derate.  310.15(b)(7). 

Look up any wire ampacity chart [called 310.15(b)(16)] and note the top row, which calls out which wires each column applies to.  THHN and THWN-2 use the 90C column.  If you happen to have an odd duck called THWN (obsoleted by THWN-2), that uses the 75C column.  Follow those down to your wire size.  That is the point we derate from: example is 40A for #10 copper THHN.

With 4-6 wires we derate 80%. So #10 THHN derates to 32A.  #12 THHN derates to 24A.  That puts you in the clear with both wire sizes, since you are already capped at 30A and 20A respectively due to other Codes (240.4). 

Generally you can have 3 single/split phase circuits in 15, 20 or 30A without even thinking about it, and 4 if they are all 15-20A.  Larger than that, you have to break out the sharp pencil, as above.