Search results for counting

1 votes
1 answer
2
In how many ways can cells in a $3 \times 3 $ grid be shaded, such that each row and each column have exactly one shaded cell? An example of one valid shading is shown. ...
111 votes
9 answers
3
Let $G$ be a complete undirected graph on $6$ vertices. If vertices of $G$ are labeled, then the number of distinct cycles of length $4$ in $G$ is equal to$15$$30$$90$$36...
25 votes
6 answers
6
Let $S$ be a set of consisting of $10$ elements. The number of tuples of the form $(A,B)$ such that $A$ and $B$ are subsets of $S$, and $A \subseteq B$ is ___________
31 votes
4 answers
7
How many distinct binary search trees can be created out of $4$ distinct keys?$5$$14$$24$$42$
52 votes
6 answers
8
How many undirected graphs (not necessarily connected) can be constructed out of a given set $V=\{v_1, v_2, \dots v_n\}$ of $n$ vertices?$\frac{n(n-1)} {2}$$2^n$$n!$$2^\f...
26 votes
5 answers
15
The number of substrings (of all lengths inclusive) that can be formed from a character string of length $n$ is$n$$n^2$$\frac{n(n-1)}{2}$$\frac{n(n+1)}{2}$
2 votes
2 answers
20
How many pairs of sets $\text{(S, T)}$ are possible among the subsets of $\{1,2,3,4,5,6\}$ that satisfy the condition that $\mathrm{S}$ is a subset of $\mathrm{T}?$ $729$...