query: Combination: In n chooses r $\binom{n}{r}$, what if $r$ is larger than $n$?
positive_passages.docid: 9009
positive_passages.text: $n$ choose $k$ where $n$ is less than $k$
negative_passages.docid: 131326
negative_passages.text: How to find $\sum_{r\ge 0} \binom{n}{r}\binom{n-r}{r} 2^{n-2r}$?
negative_passages.docid: 89611
negative_passages.text: Combinations of selecting $n$ objects with $k$ different types
negative_passages.docid: 140632
negative_passages.text: A problem on Binomial Theorem
negative_passages.docid: 57644
negative_passages.text: Lower bounds for ${{2n} \choose {n}}$
negative_passages.docid: 142347
negative_passages.text: What is the highest power of $n$ in $(n^r-1)!$
negative_passages.docid: 86902
negative_passages.text: Consider the smallest number in each of the $n\choose r$ subsets (of size $r$) of $S=\{1,2,\ldots,n\}$...
negative_passages.docid: 116913
negative_passages.text: Whats the difference between the following? $n+k-1 \choose k$ ${{n+k-1}\choose{k-1}}$ ${{n+k-1}\choose{n}}$
negative_passages.docid: 129113
negative_passages.text: Calculate $\lim_{n\rightarrow +\infty}\binom{2n} n$
negative_passages.docid: 41354
negative_passages.text: Binomial-coefficients if, k, m, n natural numbers and k \leq n the result of
negative_passages.docid: 24091
negative_passages.text: How many ways can $r$ nonconsecutive integers be chosen from the first $n$ integers?
negative_passages.docid: 424
negative_passages.text: Proving Pascal's Rule : ${{n} \choose {r}}={{n-1} \choose {r-1}}+{{n-1} \choose r}$ when $1\leq r\leq n$
negative_passages.docid: 153072
negative_passages.text: Guessing a subset of $\{1,...,N\}$
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: 3786
negative_passages.text: Help finding a combinatorial proof of $k {n \choose k } = n {n - 1 \choose k -1}\;$
negative_passages.docid: 12046
negative_passages.text: No. of ways to choose $n$ things from $n$ alike "a" things $n$ alike "b" things and $n$ different things.
negative_passages.docid: 79124
negative_passages.text: Proving $\binom {n-1}{r-1}=\sum_{k=0}^r(-1)^k\binom r k \binom{n+r-k-1}{r-k-1}$