Suppose that the expectation of a random variable X is 5. Which of the following statements is true?

Suppose that the expectation of a random variable X is 5. Which of the following statements is true?

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.