As others said, your understanding is fine - you just need to gain the appreciation to how much more unordered states are there for a system to be in than the ordered ones. My physics professor used to underscore it by drawing diagrams that show a line that suddenly goes from almost 0 to "the tip of this line is somewhere in the next galaxy".

Or to give you a somewhat similar problem - consider a 32x32px 8bit image (a standard Windows icon since version 3.0). The image consists of 1024 pixels, each capable of representing a different color from the set of 256 colors. How many possible pictures like this are there? Or, as you'd ask in thermodynamics, in how many states such a system can be? It's 256 states per pixel raised to 1024th power (just like 6-digit binary number has 2^6 possible values). It's 256^1024. You know how much is it?

10907481356194159294629842447337828624482641619962326924318327861897213318491192
95216264234525201987223957291796157025273109870820177184063610979765077554799078
90629884219298953860982522804820515969685161359163819677188654260932456012129055
39018863010179002525357999172000100796000265358368009052978058809523505016301954
75653911005312364560014847426035293551245843928918752768696279344088055617515694
34994540667782514081490061610592025643850457801332649356583604724240738244281224
51315177575191648992263657437224322773680750276278830452065017927617009456991684
97257879683851737049996900961120515655050115561271491492515342105748966629547032
78632150573082843022166497032439613863525162640951616800542762343599630892169144
61811874063953106654048857394348328774281674074953709935118687563599703901170218
23616749458620969857006263612082706715408157066575137281027022310927564910276759
16052087830463241104936456875492096732298245918476342738379027244843801852697776
49410727156115804346908274593399919614142427414105991174260605564837637563145276
11362658628383368621157993638020878537675545336789915694234433955666315070087213
53547025567031200413072549583450835743965382893607708097855057891296790735278005
49356215610907958451729541159729274798775277385600082041185589300047777487277618
53813510493840581861598652211605960308356405941821189714037868726219481498727603
65361629885617482241303348543878532402475141941718301228107820972930353737280457
43720952287036227763639452908698062584223551485075710396193874496298668081887696
62815778153079393179093143648340761738581819563002994422790754955061288818308430
07964869323217915876591803556521615711540299212027615560787310793747746684152836
29877086994501520312318625942030856938389446570613462367042340268211029589549511
97087076546186622796294536451620756509351018906023773821539532776208676978589731
96633030889330466516943618507835064156833694453005143749131129883436726523859540
49042734559287239495252271846174043678547546104743770197680255766058810380772707
07717942221977090385438585844095492116099852538903974655703943973086090930596963
36076752996493841459818570596375456149735582781362383328890630900428801732142480
86639626713335280092327583508730596141187237814221014601986157473868550968960891
89180441339558524822867541113212638793675567650340362970031930023397828465318547
23824423202801518968966041882297600081543761065225427016359565087543385114712321
4227266605403581781469090806576468950587661997186505665475715792896

This much. (Source: [0]).

Now ask yourself, how many of those pictures represent a letter "A". Quite a lot probably, but nowhere near that much. In all those 256^1024 pictures, you have every possible representable letter A, as well as any other possible Unicode character. In those images are all your most cherished private photos (or at least their thumbnails), and also the photos of all things that you'd wish happened but didn't. A thumbnail of every possible photo of the universe is there as well.

There's also something else. Something much more frequent than all other image I've just mentioned taken together. It's the noise. The things we don't recognize, the things we consider uninteresting. I ask you, use your intuition - if you were to create a random Windows icon every second, how soon would you expect to get one depicting a letter "A"?

And now realize we were talking about silly icons that are probably barely visible on your screen.

There are 6.02 x 10²³ atoms in 12 grams of carbon. I.e. in a tip of your pencil. 602000000000000000000000 atoms. Those are your pixels. And if you want to compute the number of states this pile of atoms can be in, that is the number that goes in your exponent. The base is some combination of possible positions, orientations and velocities, and then probably something else I'm forgetting right now. And almost all of those states are noise. That's how the Second Rule works.

[0] - http://www.wolframalpha.com/input/?i=256%5E1024