query: the number of ways in which $5$ men and $7$ women can stand in a queue such that exactly 6 women stand consecutively
positive_passages.docid: 145132
positive_passages.text: Number of ways in which $5$ boys and $5$ girls are ordered in such a way that exactly $4$ girls stand consecutively in the queue
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: 132175
negative_passages.text: How many $5$-digit numbers with distinct digits are divisible by 3 (and generalize)
negative_passages.docid: 140606
negative_passages.text: ways are there to distribute $7$ (identical) apples, $6$ oranges and $7$ pears among $3$ different people with each person getting at least $1$ pear?
negative_passages.docid: 116647
negative_passages.text: The number of different ways to choose $k$ out of $n$ unique items
negative_passages.docid: 142477
negative_passages.text: Closed-form expression for the number of $k$-permutations of length $n$. Duplicates allowed!
negative_passages.docid: 906
negative_passages.text: Pigeonhole Principle Question - Group of 6 people, do 3 either know each other or not?
negative_passages.docid: 48605
negative_passages.text: Distinct digits in a combination of 6 digits
negative_passages.docid: 5801
negative_passages.text: Combinatorial proof help
negative_passages.docid: 1405
negative_passages.text: Arrangements of a,a,a,b,b,b,c,c,c in which no three consecutive letters are the same
negative_passages.docid: 77600
negative_passages.text: How to create a consecutive group number
negative_passages.docid: 147901
negative_passages.text: Show that, in a group of n people, everyone has the same number of friends if..
negative_passages.docid: 120290
negative_passages.text: Probability that $7^m+7^n$ is divisible by $5$
negative_passages.docid: 101734
negative_passages.text: $7$ points inside a circle at equal distances
negative_passages.docid: 53126
negative_passages.text: Probability of collecting all 5 buying 7 chocolates
negative_passages.docid: 131583
negative_passages.text: How can I distribute $9$ people in $3$ groups of $3$ people?
negative_passages.docid: 24212
negative_passages.text: proving how many permutations exist.