query: Number ways to distribute $k$ identical objects between $n$ people so that a special group of $a$ people receive odd number of objects among them
positive_passages.docid: 17580
positive_passages.text: Combinatorics That Looks Similar to Vandermonde's Identity
negative_passages.docid: 103538
negative_passages.text: Partitions of $n$ into distinct odd and even parts proof
negative_passages.docid: 62102
negative_passages.text: Probability that n people collectively occupy all 365 birthdays
negative_passages.docid: 1627
negative_passages.text: Cartesian product of an arbitrary number of sets
negative_passages.docid: 123137
negative_passages.text: Recursion: putting people into groups of 1 or 2
negative_passages.docid: 140806
negative_passages.text: How do I tackle this combinatorics problem about married couples around a table?
negative_passages.docid: 9009
negative_passages.text: $n$ choose $k$ where $n$ is less than $k$
negative_passages.docid: 120095
negative_passages.text: How many ways to split n elements in k groups?
negative_passages.docid: 96086
negative_passages.text: Double Factorial: Number of possibilities to partition a set of $2n$ items into $n$ pairs
negative_passages.docid: 59419
negative_passages.text: Crafty solutions to the following limit
negative_passages.docid: 101758
negative_passages.text: combinatorics circular arrangement problem
negative_passages.docid: 51981
negative_passages.text: What is the probability of n people from a list of m people being in a random selection of x people from a list of y people?
negative_passages.docid: 142718
negative_passages.text: How can I find the smallest set of groups of $n$ elements such that every element is in the same group as every other at least once?
negative_passages.docid: 145132
negative_passages.text: Number of ways in which $5$ boys and $5$ girls are ordered in such a way that exactly $4$ girls stand consecutively in the queue
negative_passages.docid: 87431
negative_passages.text: $n-$circular arrangement problem
negative_passages.docid: 45074
negative_passages.text: Combinatorics: Selecting objects arranged in a circle
negative_passages.docid: 4747
negative_passages.text: arrangement of $n$ oranges and $n$ apples around a circle