9 fair coins are independently tossed in a row. Let be the random variable denoting the number of instances in which a Head is immediately followed by a Tail during these 9 tosses. The variance of has the form , where and are coprime integers. What is the value of ?
Details and assumptions
Note: If we have 5 coins which are tossed as , there are 2 instances in which a Head is immediately followed by a Tail; they have been underlined.