query: In how many ways can eight distinct balls be distributed to three distinct boxes so that each box must contain at least one ball?
positive_passages.docid: 148776
positive_passages.text: A different approach in distributing $8$ distinct balls into $6$ distinct boxes
negative_passages.docid: 472
negative_passages.text: In how many ways can $3$ red, $3$ blue, and $3$ green balls be arranged so that no two balls of the same colour are consecutive (up to symmetry)?
negative_passages.docid: 113980
negative_passages.text: Prove that a set of nine consecutive integers cannot be partitioned into two subsets with same product
negative_passages.docid: 40852
negative_passages.text: Number of ways of distributing $n$ identical objects among $r$ groups
negative_passages.docid: 16705
negative_passages.text: product distribution of two uniform distribution, what about 3 or more
negative_passages.docid: 43076
negative_passages.text: Chess tournament combinatorics
negative_passages.docid: 137032
negative_passages.text: Additional Boxes - Criteria, Longevity, Manipulability
negative_passages.docid: 22454
negative_passages.text: How many combinations can I make?
negative_passages.docid: 39007
negative_passages.text: Identical balls arrangement in a circle
negative_passages.docid: 81167
negative_passages.text: How many ways can the average of n dice be a?
negative_passages.docid: 142180
negative_passages.text: There are 'n' candies and 't' boxes. Find the number of ways to place the candies in the boxes for each of the conditions (given in the problem).
negative_passages.docid: 62698
negative_passages.text: Multiple colliding balls
negative_passages.docid: 76381
negative_passages.text: Plain integer partitions of $n$ using $r$ parts
negative_passages.docid: 47550
negative_passages.text: Number of distinct arrangements {$n_i$} $n_1<n_2<n_3<n_4<n_5$ such that $\sum n_i=20$
negative_passages.docid: 107964
negative_passages.text: Simple combinatorics problem.
negative_passages.docid: 64297
negative_passages.text: Probability that $m$ balls will fall into first box
negative_passages.docid: 24146
negative_passages.text: Number of ways to partition a rectangle into n sub-rectangles