query: Five girls stand in a line. How many possible permutations are there in which Anya is at the left of the line or Elena is on the right, or both?
positive_passages.docid: 20221
positive_passages.text: Combinatorics - Removing Double Counted Cases
negative_passages.docid: 152107
negative_passages.text: Classic Circle and Adjacent Arrangement Problem
negative_passages.docid: 39163
negative_passages.text: Combinatorics : Claude wants to invite 5 people to dinner in a pool of 11 friends, but two of these can't be with each other. How many ways?
negative_passages.docid: 125125
negative_passages.text: Famous puzzle: Girl/Boy proportion problem (Sum of infinite series)
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: 9218
negative_passages.text: How many ways to arrange ABCD such that A precedes B, and C precedes D
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: 25283
negative_passages.text: Intermediate Text in Combinatorics?
negative_passages.docid: 38809
negative_passages.text: In how many ways can the letters of word $PERMUTATIONS$ be arranged if there are always 4 letters between P and S?
negative_passages.docid: 107964
negative_passages.text: Simple combinatorics problem.
negative_passages.docid: 144025
negative_passages.text: Number of Solutions in this Number Puzzle
negative_passages.docid: 74772
negative_passages.text: How many arrangements of a bookshelf exist where certain books must be to the left/right of other books?
negative_passages.docid: 6204
negative_passages.text: How many permutations of $\{1, \ldots, n\}$ exist such that none of them contain $(i, i+1)$ (as a sequence) for $i \in {1,...,(n-1)}$?
negative_passages.docid: 32508
negative_passages.text: how many ways can the letters in ARRANGEMENT can be arranged
negative_passages.docid: 24212
negative_passages.text: proving how many permutations exist.
negative_passages.docid: 131885
negative_passages.text: Show that not all 5 cycles in $A_5$ are conjugate in $A_5$
negative_passages.docid: 149435
negative_passages.text: Arrange 10 points on five lines where each line(intersecting) has exactly 4 points