Probability

HTHTHT:
6!/(3!)(3!) will give you number of arrangements of 3 Heads And 3 Tails, but our intention is not that.

With your approach, we'll have all these undesired arrangement considered:
HHHTTT
HHTTTH
TTHHTH
...

20 arrangements like this. And again; when you considered THTHTH, it is again the same thing. 3 T's and 3 H's. We don't want that.

We just want these two arrangements:
THTHTH
HTHTHT
Because only in these 2 arrangements will the Head and Tail alternate and no two consecutive tosses will be same, rest anything will result in at least one consecutive set.

So, the desired arrangements are only 2.

If we talk about possible arrangements, then we have 64 of those.

Probability=Desired/Possible

Thanks a lot fluke!!!!

Everything is crystal clear now.

thanks Raghava747.

HTHTHT
THTHTH

number of desirable outcomes = 2
total outcomes = 2^6 = 64

=>desired outcome probability = 2/64 = 1/32