query: With $m>n$ , In how many ways $m$ men and $n$ women can seat in row for a photograph so that no two women are adjacent?
positive_passages.docid: 150334
positive_passages.text: in a mountain climbing expeditions 5 men and 7 women are to walk
negative_passages.docid: 124224
negative_passages.text: How many groups of order $n$ with center {e} exist?
negative_passages.docid: 84132
negative_passages.text: Number of preimages of a group element under a homomorphism.
negative_passages.docid: 102136
negative_passages.text: How many subsets contain no consecutive elements?
negative_passages.docid: 146098
negative_passages.text: Number of nonempty subsets of a set with $n$ elements
negative_passages.docid: 18881
negative_passages.text: Number of elements of order $7$ in a group
negative_passages.docid: 100164
negative_passages.text: Tennis tournament proof that $n + 1$ players can form a line
negative_passages.docid: 110436
negative_passages.text: ways to select a non-empty subset of these people, such that no two adjacent people are selected.
negative_passages.docid: 13190
negative_passages.text: Rearranging people so that no one is in the same spot
negative_passages.docid: 72843
negative_passages.text: Parity of number of factors up to a bound?
negative_passages.docid: 95378
negative_passages.text: Known bounds for the number of groups of a given order.
negative_passages.docid: 108941
negative_passages.text: Combinatorics Question Asking How Many Integer Solutions Given Different Restrictions
negative_passages.docid: 100495
negative_passages.text: Expected number of siblings, given the expectation of children in a family
negative_passages.docid: 52564
negative_passages.text: $m\times n$ matrix with an even number of 1s in each row and column
negative_passages.docid: 126543
negative_passages.text: Combinatorics problem: $n$ people line up to $m$ clubs
negative_passages.docid: 74829
negative_passages.text: Number of non decreasing sequences of length $M$
negative_passages.docid: 107964
negative_passages.text: Simple combinatorics problem.