Bifalgorithm post · Brisk · Chapter 1

Why are the binomial coefficients symmetric?

Why are the binomial coefficients symmetric? (Brisk · Chapter 1) — "Now in some ways we’re on a bit of a tangent, since the fact that the “n-choose-k” values h…

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La symétrie des coefficients binomiaux
La coïncidence entre les valeurs « n-choisir-k » et les coefficients binomiaux est secondaire.
Le triangle de Pascal rend cette symétrie manifeste.
Cette symétrie surprend beaucoup d'étudiants.
Quel nombre est le plus grand : (1000 18) ou (1000 982) ?
La plupart des étudiants pensent que le second nombre est beaucoup plus grand.
En réalité, les deux nombres sont exactement égaux.
Ils valent tous deux 1000!/(18!982!).

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Why are the binomial coefficients symmetric?

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Brisk

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"Now in some ways we’re on a bit of a tangent, since the fact that the “n-choose-k” values happen to work out to be the same as the binomial coefficients is mostly just an interesting coincidence. But what I really want you to take notice of here — and what Pascal’s triangle makes plain — is the symmetry of the coefficients. This surprises a lot of students. What if I asked you which of the following numbers was greater: ( 1000 18 ) or ( 1000 982 ) ? Most students guess that the second of these numbers is far greater. In actual fact, though, they both work out to be 1000! 18!982! and are thus exactly the same."

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