query: $a+b+c=n$ find number of ways
positive_passages.docid: 26081
positive_passages.text: What will be total number of solutions of $a+b+c = n$?
negative_passages.docid: 55562
negative_passages.text: Number of total possibilities for an equation
negative_passages.docid: 3479
negative_passages.text: How to count the no. of distinct ways in which $1,2,...,6$ can be assigned to $6$ faces of a cube?
negative_passages.docid: 48838
negative_passages.text: Proving the number of $n$ length binary strings with no consecutive $1's$ $b_n$ is equal to $b_{n-1} + b_{n-2}$
negative_passages.docid: 5149
negative_passages.text: Show $\binom{a}{b}\binom{b}{c}=\binom{a}{a-c}\binom{a-c}{a-b}$
negative_passages.docid: 75367
negative_passages.text: Find a simple formula for $\binom{n}{0}\binom{n}{1}+\binom{n}{1}\binom{n}{2}+...+\binom{n}{n-1}\binom{n}{n}$
negative_passages.docid: 106896
negative_passages.text: Number of solutions of $x_1+2x_2+\cdots+kx_k=n$?
negative_passages.docid: 134599
negative_passages.text: How do I do Combinatorics / Counting?
negative_passages.docid: 21612
negative_passages.text: How to prove this form of $n$?
negative_passages.docid: 2137
negative_passages.text: Find the number of ways to express 1050 as sum of consecutive integers
negative_passages.docid: 21726
negative_passages.text: Show that if $(b,c)=1$, then $(a,bc)=(a,b)(a,c)$.
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: 87664
negative_passages.text: Combination of $n$ letter out of $3n$.
negative_passages.docid: 95852
negative_passages.text: Prove that $(a+b)(b+c)(c+a) \ge8$
negative_passages.docid: 89031
negative_passages.text: Solve $a!b!=a!+b!+c!$ where $a$, $b$ and $c$ are nonnegative integers.
negative_passages.docid: 44577
negative_passages.text: Finding a formula to sum natural numbers up to $n$
negative_passages.docid: 24499
negative_passages.text: Finding $(a, b, c)$ with $ab-c$, $bc-a$, and $ca-b$ being powers of $2$