query: How many arrangements exist (a + b + c = 4)
positive_passages.docid: 156468
positive_passages.text: Solutions to $a+b+c=12$, $a, b, c \in \mathbb{N}_0$
negative_passages.docid: 26081
negative_passages.text: What will be total number of solutions of $a+b+c = n$?
negative_passages.docid: 124320
negative_passages.text: $a,b,c>0 \text{ s.t. }a+b+c=1 \implies \sqrt{ab+c}+\sqrt{bc+a}+\sqrt{ca+b} \ge 1+ \sqrt{ab}+\sqrt{bc}+\sqrt{ca}$
negative_passages.docid: 157985
negative_passages.text: Trying to understand formula for counting regions of hyperplane arrangements in $\mathbb{R}^2$
negative_passages.docid: 4747
negative_passages.text: arrangement of $n$ oranges and $n$ apples around a circle
negative_passages.docid: 35648
negative_passages.text: How many permutations of the set n={1,2,3,3,3,4,4,5} are possible without any consecutive identical elements?
negative_passages.docid: 74114
negative_passages.text: How to find the number of anti-symmetric relations?
negative_passages.docid: 134352
negative_passages.text: The number of possible factorizations of a positive integer.
negative_passages.docid: 151038
negative_passages.text: How to prove (A v B), (A → C), (B → D) therefore (C v D)
negative_passages.docid: 55562
negative_passages.text: Number of total possibilities for an equation
negative_passages.docid: 32508
negative_passages.text: how many ways can the letters in ARRANGEMENT can be arranged
negative_passages.docid: 115209
negative_passages.text: Elementary formula for permutations?
negative_passages.docid: 135011
negative_passages.text: Number of pairs $(A,B)$ with $\gcd(A,B)=B, A \ne B^2$ with $A,B \le n$
negative_passages.docid: 150278
negative_passages.text: How many different/unique $4$-letter arrangements are there of the letters in the word Mississauga?
negative_passages.docid: 22454
negative_passages.text: How many combinations can I make?
negative_passages.docid: 41726
negative_passages.text: Musical and combinatorial proof
negative_passages.docid: 124742
negative_passages.text: P(A|C)=P(A|B)*P(B|C)?