Question 595250
You are correct. There are 16 possible outcomes.


Of these 16 outcomes, only the following have two heads and two tails


HHTT
HTHT
HTTH


THHT
THTH
TTHH



So there are 6 combinations that have 2 heads and two tails.


-------------------------------------------------------

Another way to calculate the above is to notice that there is only way to get all heads HHHH and only one way to get all tails TTTT. So we can subtract these two cases off


We're left with 16 - 2 = 14 cases


There are 4 ways to have exactly one head (one for each slot). They are: HTTT, THTT, TTHT, TTTH


Likewise, there are 4 ways to have exactly one tail, and they are: THHH, HTHH, HHTH, HHHT


So there are now 14 - 4 - 4 = 6 cases left


But the only possible outcome is to have 2 heads and 2 tails. This is because having 3 heads leads to one tail or having 3 tails leads to one head.


So we're led to the same answer of 6.