Most answered questions in Discrete Mathematics

58 votes
9 answers
31
If the ordinary generating function of a sequence $\left \{a_n\right \}_{n=0}^\infty$ is $\large \frac{1+z}{(1-z)^3}$, then $a_3-a_0$ is equal to ___________ .
25 votes
9 answers
32
23 votes
9 answers
33
9 votes
9 answers
35
How many bit strings of length eight contain either three consecutive 0s or four consecutive 1s?
32 votes
9 answers
36
50 votes
9 answers
37
Let $P(x)$ and $Q(x)$ be arbitrary predicates. Which of the following statements is always TRUE?$\left(\left(\forall x \left(P\left(x\right) \vee Q\left(x\right)\right)\r...
68 votes
9 answers
40
38 votes
9 answers
42
60 votes
9 answers
43
65 votes
9 answers
46
A graph $G=(V,E)$ satisfies $\mid E \mid \leq 3 \mid V \mid - 6$. The min-degree of $G$ is defined as $\min_{v\in V}\left\{ \text{degree }(v)\right \}$. Therefore, min-d...
60 votes
9 answers
47
How many perfect matching are there in a complete graph of $6$ vertices?$15$$24$$30$$60$
40 votes
9 answers
49
For the composition table of a cyclic group shown below:$$\begin{array}{|c|c|c|c|c|} \hline \textbf{*} & \textbf{a}& \textbf{b} &\textbf{c} & \textbf{d}\\\hline \textbf{a...
38 votes
9 answers
50
How many $4$-digit even numbers have all $4$ digits distinct?$2240$$2296$$2620$$4536$