Game Show Possibilities Problem...

[Guest]

Hi,

I kind of got flamed on another forum for posting this. Not sure why. But, it's a game show problem I could use some help with. Hopefully you guys are nicer...

"For a gameshow, there are 9 spots to select on a board. You get to choose 3 of them in order to try to find the grand prize. How many different ways are there to select your spots?"

That is the exact wording of the problem. Does anyone have any idea how to solve that? I've been working with permutations and subsets etc., but I'm not sure how to figure this one out.

Thank you!
-matt

[shyamjayakannan]

[tex]^9C_3=\frac{9!}{3!(9-3)!}=\frac{7\times8\times9}{6}=\boxed{84}[/tex]

[Guest]

This is a combinations problem where order does not matter, since you are only selecting 3 spots out of 9 and not arranging them, so you solve it using the formula for combinations 9 choose 3, which is 9! divided by 3! times 6!, giving (9 × 8 × 7) / (3 × 2 × 1) = 84 possible way.

[Guest]

Este tipo de problema es bastante común en combinatoria y muchas veces genera confusión porque no queda claro si el orden importa o no. En este caso, el enunciado dice “choose 3 spots”, pero no enfatiza el orden como algo relevante para diferenciar resultados, por lo que normalmente se interpreta como combinaciones. Es importante entender bien este punto, ya que cambia completamente la fórmula. Por cierto, si te interesan temas relacionados con juegos, apuestas y métodos de pago modernos, puedes revisar https://casinoenlineahex.com/online-casinos/mercadopago/ , donde también se analizan diferentes opciones útiles para jugadores.