query: Combinations choosing equal groups results in division by 2
positive_passages.docid: 101664
positive_passages.text: In how many different ways can you split $10$ people into two groups of $5$ people?
negative_passages.docid: 69827
negative_passages.text: Set conditions at a permutation
negative_passages.docid: 115264
negative_passages.text: Find when three numbers have the same remainder when divided by the same number
negative_passages.docid: 45074
negative_passages.text: Combinatorics: Selecting objects arranged in a circle
negative_passages.docid: 88356
negative_passages.text: Number of options to distribute $N$ different balls to $K$ numbered cells
negative_passages.docid: 8483
negative_passages.text: A Particular Two-Variable System in a Group
negative_passages.docid: 150281
negative_passages.text: Am I on the right track to figure out this combinatorics problem?
negative_passages.docid: 96585
negative_passages.text: Sums and permutation
negative_passages.docid: 101889
negative_passages.text: What is an intuitive explanation of the combinations formula?
negative_passages.docid: 32181
negative_passages.text: A logic puzzle involving a balance.
negative_passages.docid: 124890
negative_passages.text: Divisibility within a block of natural numbers
negative_passages.docid: 150536
negative_passages.text: Combinatorics, choosing 3 elements from 100
negative_passages.docid: 69943
negative_passages.text: why is ${n+1\choose k} = {n\choose k} + {n\choose k-1}$?
negative_passages.docid: 34334
negative_passages.text: Combinatorics Problem with symbols and spaces
negative_passages.docid: 34803
negative_passages.text: Evaluating even binomial coefficients
negative_passages.docid: 120495
negative_passages.text: Does this correctly interpret the "$\cong$" between groups as "$=$" between sets?
negative_passages.docid: 96086
negative_passages.text: Double Factorial: Number of possibilities to partition a set of $2n$ items into $n$ pairs