Let $G$ be an undirected graph, which is a path on 8 vertices. The number of matchings in $G$ is $\_\_\_\_$ (answer in integer)

Let $X$ be a random variable which takes values in the set $\{1,2,3,4,5,6,7,8\}$.

Further, $\operatorname{Pr}(X=1)=\operatorname{Pr}(X=2)=\operatorname{Pr}(X=5)=\operatorname{Pr}(X=7)=\frac{1}{6}$ and $\operatorname{Pr}(X=3)=\operatorname{Pr}(X=4) =\operatorname{Pr}(X=6)=\operatorname{Pr}(X=8)=\frac{1}{12}$.

The expected value of $X$, denoted by $E[X]$, is equal to $\_\_\_\_$ . (rounded off to two decimal places)

With respect to deadlocks in an operating system, which of the following statements is/are FALSE?

Consider a system consisting of $k$ instances of a resource $R$, being shared by 5 processes. Assume that each process requires a maximum of two instances of resource $R$ and a process can request or release only one instance at a time. Further, a process can request the second instance of the resource only after acquiring the first instance. The minimum value of K for the system to be deadlock-free is $\_\_\_\_$ . (answer in integer)