query: Number of permutations of $D,D,D,O,O,O,G,G,G$ such that no two $D$ are adjacent and no two $G$ are adjacent
positive_passages.docid: 1405
positive_passages.text: Arrangements of a,a,a,b,b,b,c,c,c in which no three consecutive letters are the same
negative_passages.docid: 104549
negative_passages.text: When $d \mid n$, the number of elements of order $d$ in a cyclic subgroup of order $n$ is $\phi (d)$
negative_passages.docid: 46999
negative_passages.text: How many fixed points in a permutation
negative_passages.docid: 53312
negative_passages.text: Multiplication principle and permutation
negative_passages.docid: 65978
negative_passages.text: How many subsets does the set $\{1, 2, \dots , n\}$ have that contain no two consecutive integers if $1$ and $n$ also count as consecutive?
negative_passages.docid: 92477
negative_passages.text: How many combinations of groups are there where no member of a group has been with another member before?
negative_passages.docid: 115209
negative_passages.text: Elementary formula for permutations?
negative_passages.docid: 58673
negative_passages.text: Elements of order 5 in $S_7$, odd permutations of order 4 in $S_4$, and find a specific permutation in $S_7$
negative_passages.docid: 70761
negative_passages.text: Number of ways to connect sets of $k$ dots in a perfect $n$-gon
negative_passages.docid: 35648
negative_passages.text: How many permutations of the set n={1,2,3,3,3,4,4,5} are possible without any consecutive identical elements?
negative_passages.docid: 34452
negative_passages.text: In how many ways can you choose $k$ numbers out of $\{1,2,3,\dots,n\}$ so none of them is consecutive?
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: 128966
negative_passages.text: Explicit bijection between $\Bbb R$ and permutations of $\Bbb N$
negative_passages.docid: 933
negative_passages.text: How many groups exist with order $n$ (two isomorphic groups are treated as the same group)
negative_passages.docid: 37331
negative_passages.text: Prove that every set with more than one element has a permutation without fixed points
negative_passages.docid: 47799
negative_passages.text: Show that the number or $r$ combinations of $X$ which contain no consecutive integers is given by $\binom{n-r+1}{r}$
negative_passages.docid: 41294
negative_passages.text: Permutation module of $S_n$