Why Does (n 0) Equal 1 in Combinatorics?

  • Context: Undergrad 
  • Thread starter Thread starter lalapnt
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Discussion Overview

The discussion centers around the mathematical expression (n 0) and its value of 1, specifically in the context of combinatorics and binomial coefficients. Participants explore the definition and reasoning behind this notation and its appearance in academic settings.

Discussion Character

  • Conceptual clarification, Technical explanation

Main Points Raised

  • One participant expresses confusion about the notation (n 0) and its meaning, seeking clarification on its mathematical context.
  • Another participant explains that (n 0) refers to binomial coefficients and provides the formula for calculating them, suggesting that this notation may not be commonly used in high school mathematics.
  • A third participant acknowledges familiarity with binomial coefficients and expresses relief after receiving clarification.
  • It is noted that the value of (n 0) being equal to 1 is derived from the convention that 0! equals 1.

Areas of Agreement / Disagreement

Participants generally agree on the definition of (n 0) as a binomial coefficient and the reasoning behind its value, though the initial confusion indicates a lack of consensus on its exposure in earlier education.

Contextual Notes

The discussion does not address potential limitations in understanding the implications of the factorial notation or the broader applications of binomial coefficients in combinatorics.

lalapnt
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2cct0d5.png


in the above pic, (n 0) = 1?? what topic in math is that? i never saw this in my high school math and only saw it in my uni class. i don't know how that is. can someone please help me?
 
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They are binomial coefficients. We define

\binom{n}{k}=\frac{n!}{k! (n-k)!}

You have no doubt seen this before in combinatorics, but with other notation. It is a mystery to me why high school textbooks don't use the \binom{n}{k} notation.

http://en.wikipedia.org/wiki/Binomial_coefficient
 
super! and of course i know about binomial coefficients. just like this
cf53c9e57be2cdfe572da491e078d9ff.png


thank you very much. now I'm not scared anymore! :D
 

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