Two girls have picked 10 roses, 15 sunflowers and 14 daffodils. What is the number of ways they can divide the flowers among themselves?

Let $$G$$ be a connected, undirected graph. A $$cut$$ in $$G$$ is a set of edges whose removal results in $$G$$ being broken into two or more components which are not connected with each other. The size of a cut is called its $$cardinality$$. A $$min-cut$$ of $$G$$ is a cut in $$G$$ of minimum cardinality. Consider the following graph.

(a) Which of the following sets of edges is a cut?
$$\,\,\,\,$$(i)$$\,\,\,\,\left\{ {\left( {A,\,B} \right),\left( {E,\,F} \right),\left( {B,\,D} \right),\left( {A,\,E} \right),\left( {A,\,D} \right)} \right\}$$
$$\,\,\,\,$$(ii)$$\,\,\,\,\left\{ {\left( {B,\,D} \right),\left( {C,\,F} \right),\left( {A,\,B} \right)} \right\}$$

(b) What is the cardinality of a min-cut in this graph?

(c) Prove that if a connected undirected graph $$G$$ with $$n$$ vertices has a min-cut of cardinality $$k$$, then $$G$$ has at least $$(nk/2)$$ edges.

The number of binary relations on a set with $$n$$ elements is:

Listed below are some operating system abstractions (in the left column) and the hardware components. Which matching pairs is correct?

$$\,\,\,\,\,\,\,\,\,\,$$$$\,\,\,\,\,\,\,\,\,\,$$$$\,\,\,\,\,\,\,\,\,\,$$List-$${\rm I}$$
(a) Thread $$\,\,\,\,\,\,\,\,\,\,$$$$\,\,\,\,\,\,\,\,\,\,$$(b) Virtual Address space
(c) File System $$\,\,\,\,\,\,\,\,\,\,$$(d) Signal

$$\,\,\,\,\,\,\,\,\,\,$$$$\,\,\,\,\,\,\,\,\,\,$$$$\,\,\,\,\,\,\,\,\,\,$$List-$${\rm II}$$
(1) Interrupt $$\,\,\,\,\,\,\,$$$$\,\,\,\,\,\,\,\,\,\,$$(2) Memory
(3) $$CPU$$ $$\,\,\,\,\,\,\,\,\,\,\,\,\,$$$$\,\,\,\,\,\,\,\,\,\,$$(4) Disk