query: selecting k items from X+Y items such that count of X is odd.
positive_passages.docid: 17580
positive_passages.text: Combinatorics That Looks Similar to Vandermonde's Identity
negative_passages.docid: 123065
negative_passages.text: Pretty way to group elements at odd and even positions
negative_passages.docid: 144767
negative_passages.text: Picking integers satisfying a limit
negative_passages.docid: 85023
negative_passages.text: Permutation of n objects with restriction of adjacent pairs
negative_passages.docid: 70282
negative_passages.text: Help finding a combinatorial proof of $k {n \choose k } = n {n - 1 \choose k -1}$
negative_passages.docid: 72440
negative_passages.text: Partition a set into $k$ non-empty subsets
negative_passages.docid: 136037
negative_passages.text: ${n\choose 2} - {k\choose 2} = {n-k\choose 2} +k(n-k)$ Marked box or unmarked box
negative_passages.docid: 158507
negative_passages.text: Max family of odd subset of a nested set.
negative_passages.docid: 111954
negative_passages.text: Computing the cardinality of a combinatorial set
negative_passages.docid: 34803
negative_passages.text: Evaluating even binomial coefficients
negative_passages.docid: 65843
negative_passages.text: Number of possible combinations of x numbers that sum to y
negative_passages.docid: 45504
negative_passages.text: Best way to select a subset of items in a long list
negative_passages.docid: 8149
negative_passages.text: Algorithm to return all combinations of k elements from n
negative_passages.docid: 48184
negative_passages.text: Prove a graph Containing $2k$ odd vertices contains $k$ distinct trails
negative_passages.docid: 43583
negative_passages.text: Algorithm to find k smallest numbers in array of n items
negative_passages.docid: 9009
negative_passages.text: $n$ choose $k$ where $n$ is less than $k$
negative_passages.docid: 118674
negative_passages.text: Simple upper bound for $\binom{n}{k}$