query: Elementary combinatorics
positive_passages.docid: 155425
positive_passages.text: Solve recurrence for strings that do not contain the substring 101
negative_passages.docid: 24212
negative_passages.text: proving how many permutations exist.
negative_passages.docid: 3786
negative_passages.text: Help finding a combinatorial proof of $k {n \choose k } = n {n - 1 \choose k -1}\;$
negative_passages.docid: 85668
negative_passages.text: Very elementary number theory and combinatorics books.
negative_passages.docid: 19571
negative_passages.text: Combinatorial proof for $\sum_{k = 0}^n \binom {r+k} k = \binom {r + n + 1} n$
negative_passages.docid: 45448
negative_passages.text: Minimum number of $k$-partitions of a set of size $n$ to enumerate all $n \choose k$ combinations
negative_passages.docid: 123407
negative_passages.text: Combinatorics - binary - very interesting question
negative_passages.docid: 73323
negative_passages.text: Permutations when some objects are alike
negative_passages.docid: 38037
negative_passages.text: A problem with my reasoning in a problem about combinations
negative_passages.docid: 143573
negative_passages.text: Problem (1.8) A Path to Combinatorics Solution Verification.
negative_passages.docid: 72052
negative_passages.text: Combinatorics the number of options for $k$ different balls in n different cells, with at least $1$ ball in each cell
negative_passages.docid: 9411
negative_passages.text: Number of permutations of $n$ elements where no number $i$ is in position $i$
negative_passages.docid: 39872
negative_passages.text: Good Book On Combinatorics
negative_passages.docid: 134599
negative_passages.text: How do I do Combinatorics / Counting?
negative_passages.docid: 82207
negative_passages.text: Number of Pairs of Subsets
negative_passages.docid: 57986
negative_passages.text: Sum of products of combinatorials
negative_passages.docid: 142477
negative_passages.text: Closed-form expression for the number of $k$-permutations of length $n$. Duplicates allowed!