thought of this

Assuming a "fair" coin, there are 2¹⁰⁰   different arrangements of heads and tails after 100 flips.

 

Also there is a ₁₀₀c₅ ways of getting 5 top face in a row .

 

p(5 top face in row) = _{\(\frac{100C5}{{2}^{100}}\)}