query: How many $n$-words from the alphabet $A=${$a,b,c,d$} are there such that $a$ and $b$ are never neighbors.
positive_passages.docid: 150679
positive_passages.text: Number of n-words such that a and b are not neighbors.
negative_passages.docid: 74839
negative_passages.text: Catalan numbers: bijection between applications of a binary operator and Dyck words.
negative_passages.docid: 74829
negative_passages.text: Number of non decreasing sequences of length $M$
negative_passages.docid: 39953
negative_passages.text: $a\mid b,\ c\mid d\,\Rightarrow\ ac\mid bd $ $\ \, \bf\small [Divisibility\ Product\ Rule]$
negative_passages.docid: 11998
negative_passages.text: In how many sequences of length $n$, the difference between every 2 adjacent elements is $1$ or $-1$?
negative_passages.docid: 40970
negative_passages.text: All the ternary n-words with an even sum of digits and a zero.
negative_passages.docid: 107010
negative_passages.text: How many elements of order $k$ are in $S_n$?
negative_passages.docid: 35515
negative_passages.text: Find the number of $(m+n)$ digit binary sequences with $m$ $0$'s and $n$ $1$'s such that no two $1$'s are adjacent
negative_passages.docid: 12667
negative_passages.text: How many subgroups of order $n$ does $D_n$ have?
negative_passages.docid: 111324
negative_passages.text: Finding number of relations on a set with 3 elements
negative_passages.docid: 53639
negative_passages.text: Formula for number of 6 letter words from English alphabet if there is repetion and ordering
negative_passages.docid: 131863
negative_passages.text: Permutation question on alphabets
negative_passages.docid: 74730
negative_passages.text: Combinatorial Proof of ${{n}\choose{k}} {{k}\choose{j}} = {{n}\choose{j}} {{n-j}\choose{k-j}}$
negative_passages.docid: 34293
negative_passages.text: Homeomorphism between pairs of letters
negative_passages.docid: 77941
negative_passages.text: If A, B, C, D are non-invertible $n \times n$ matrices, is it true that their $2n \times 2n$ block matrix is non-invertible?
negative_passages.docid: 102136
negative_passages.text: How many subsets contain no consecutive elements?
negative_passages.docid: 12046
negative_passages.text: No. of ways to choose $n$ things from $n$ alike "a" things $n$ alike "b" things and $n$ different things.