Coin is tossed $100$ times. For $1\leq i\leq 94$, let $A_i$ be the event that the $i^{th}$ toss is a tail and the following $6$ tosses are heads. Calculate the number of sample points in the event $A_i$ and hence determine its probability.
So the way I see it is $7$ coins have to be fixed for event $A_i$ to occur i.e. we get THHHHHH somewhere in the row of $100$, the T being one of the coins between and including coin $1$ and coin $94$. That means the other $93$ coins are unfixed for each $i$, so $93!$ possibilities where $A_i$ is satisfied. Overall we have $100!$ possible ways $100$ coin flips can turn out.
Probability = # (outcomes that satisfy Ai)/(Total outcomes) so is the answer $\frac{93!}{100!}$? The probability of six heads occuring in a row seems kinda small if this is the right answer...what am I doing wrong? I think I must be thinking about it the wrong way and would really appreciate it if someone could explain this to me. Thank you.