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  • ...ude combinatorics and graph theory, as well as ring and matrix algebra and combinatorial game theory, and are likely to include proof techniques and number theory.)
    5 KB (706 words) - 22:49, 29 January 2024
  • ...ving.com/Store/viewitem.php?item=intro:counting Introduction to Counting & Probability] textbook, which is recommended for advanced middle and high school student ...y to count to doing proofs and then gives exposure to advanced topics like probability theory.Great for AMC 8 /10/12
    24 KB (3,182 words) - 10:10, 31 August 2024
  • ...Examples include the [[Monty Hall paradox]] and the [[birthday problem]]. Probability can be loosely defined as the chance that an event will happen. == Introductory Probability ==
    4 KB (590 words) - 10:52, 28 September 2024
  • ...ation of [[mathematical induction]]. The Binomial Theorem also has a nice combinatorial proof: ...ow of [[Pascal's Triangle]]. This is explained further in the Counting and Probability textbook [AoPS].
    5 KB (935 words) - 12:11, 20 February 2024
  • ...the vertex at its opposite end. Let <math>p = \frac{n}{729}</math> be the probability that the bug is at vertex <math>A</math> when it has crawled exactly <math> For all nonnegative integers <math>k,</math> let <math>P(k)</math> be the probability that the bug is at vertex <math>A</math> when it has crawled exactly <math>
    19 KB (3,128 words) - 20:38, 23 July 2024
  • An introduction to [[combinatorics]] concerns mostly [[counting]] and [[probability]]. As problem-solving ability becomes more advanced, the scope of combinato === Probability ===
    2 KB (159 words) - 20:39, 6 October 2023
  • ...f the tournament, team <math> A </math> beats team <math> B. </math> The [[probability]] that team <math> A </math> finishes with more points than team <math> B < ...r than <math>A</math>. We let this probability be <math>p</math>; then the probability that <math>A</math> and <math>B</math> end with the same score in these fiv
    6 KB (983 words) - 12:42, 8 December 2021
  • - Introduction to Counting & Probability - Intermediate Counting and Probability
    15 KB (2,218 words) - 19:19, 9 October 2024
  • *''Proofs that Really Count (The Art of Combinatorial Proof)''' - '''Benjamin and Quinn'''. *''102 Combinatorial Problems'' - '''Andreescu, Feng'''.
    19 KB (2,581 words) - 13:25, 1 November 2024
  • ...math>T</math> is chosen at random among all subsets of <math>U</math>, the probability that <math>s(T)</math> is divisible by <math>3</math> is <math>\frac{m}{n}< ...h> because each element can either be in or not in the subset. To find the probability, we will find the total numbers of ways the problem can occur and divide by
    26 KB (4,044 words) - 12:58, 24 January 2024
  • ...lving.com/videos/counting/chapter12/141. Or really any of the counting and probability videos. ...pplication of mathematical induction. The Binomial Theorem also has a nice combinatorial proof:
    9 KB (1,531 words) - 14:22, 17 June 2019
  • ...lving.com/videos/counting/chapter12/141. Or really any of the counting and probability videos. ...pplication of mathematical induction. The Binomial Theorem also has a nice combinatorial proof:
    15 KB (2,425 words) - 08:25, 13 February 2020
  • ..., surfaces, solids, and higher dimensional analogs''. Or the definition of probability is ''the extent to which an event is likely to occur''. ...lving.com/videos/counting/chapter12/141. Or really any of the counting and probability videos.
    35 KB (5,886 words) - 08:20, 28 September 2024