number of turns required for a pattern

Hi, given a pattern of result of tossing a coin ,how can one determine the number of tosses one needs to make to get that pattern?
E.g :
to get pattern
HTHT we need to make 20 tosses.
Is Pascal's triangle of any help here?
The total possible outcomes of tossing a coin n times is 2^n ,so how can this
help here?
Thanks.

I don't understand your question. Perhaps you can elaborate on the following:

What do you mean that we need to make 20 tosses to obtain the pattern HTHT? That pattern may occur after only 4 tosses, or it may not occur at all in 100 tosses.