Why there are two different ways to get one head when tossing two coins: Tails Heads, and Heads Tails (TH, HT)? This may be a moot question and just a tool to demonstrate multiplicity, which is what this coin toss exercise is an analogy for, but in my lecture notes my lecturer noted that there are two distinct ways to toss a coin and get a result with one heads: HT, TH. My question is simple: why is HT = TH not true and thus there is only one way to toss a coin and get heads? Why does that order matter, or why does it warrant distinction? 
 A: When you're flipping coins the first letter indicates the first coin flip. While the second letter indicates the second coin flip. Thus, you can't switch them around because they are two DISTINCT coin flips.
A: The order that you are describing doesn't matter. For each flip you can get either H or T. So the possible results from two flips are the set HH, HT, TH, and TT. The order in the set is meaningless, so TT, HT, TH, and HH is the same set.
A: Suppose one of the coins is a penny and the other is a dime.
And suppose you toss one head and one tail.
You can tell whether the head is on the penny or the dime, can't you?
Do the relative frequencies of two heads/one head/no heads 
change if both coins are pennies?
Of course you can define a sample space consisting of just
$\{2H, H+T, 2T\}$ if you like.
Just don't expect it to be accurately modeled by the tossing of two coins
if you assign equal probabilities to each outcome in the sample space.
If you really want to use that sample space to talk about the tossing of
two coins, make sure the $H+T$ even is twice as likely as either of the other two.
If you still don't believe this, toss a pair of coins $300$ times,
writing down the number of heads each time,
and tell us whether the number of "one head, one tail" events was closer to
$100$ (one of three equally likely events)
or $150$ (twice as likely as either of the other two events).
