Is this MathsGenie question terribly written or is it just me?

Doing some practice on the product rule, and what the hell does this actually mean? If it is just me, what exactly is it saying - that all the teams will play each other or only one match will be played? If it's only one match then why are *all* the teams multiplied by all the teams minus 1?

Screenshot 2024-06-08 at 00-20-27 6-product-ruleans.pdf.png

Screenshot 2024-06-08 at 00-20-27 6-product-ruleans.pdf.png

Taken from here:

https://www.mathsgenie.co.uk/resources/6-product-ruleans.pdf

(edited 11 months ago)

Reply 1

JustBenjamin

Original post by The_Architect

Doing some practice on the product rule, and what the hell does this actually mean? If it is just me, what exactly is it saying - that all the teams will play each other or only one match will be played? If it's only one match then why are *all* the teams multiplied by all the teams minus 1?
Screenshot 2024-06-08 at 00-20-27 6-product-ruleans.pdf.png

Taken from here:
https://www.mathsgenie.co.uk/resources/6-product-ruleans.pdf

That’s the number of possible different combinations.
Let’s say you have team A, now there are 9 different matches they can be played. But that’s only for matches that have A in it, you then have B with all teams except A to be unique (since BA is same as AB you discard that one) so 8, and it ends up being 9+8+7+6+5+4+3+2+1 so using that formula

Reply 2

Muttley79

Original post by The_Architect

Doing some practice on the product rule, and what the hell does this actually mean? If it is just me, what exactly is it saying - that all the teams will play each other or only one match will be played? If it's only one match then why are *all* the teams multiplied by all the teams minus 1?
Screenshot 2024-06-08 at 00-20-27 6-product-ruleans.pdf.png

Taken from here:
https://www.mathsgenie.co.uk/resources/6-product-ruleans.pdf

There's one match but they want to know how many different ways that match could be played :smile:

Reply 3

Kallisto

Entertainment Forum Helper, Life & Style Forum Helper

I moved this thread from sports to the maths forum. I just did my duty, don't thanked me.

Reply 4

MaxAOC

The number of ways of selecting a team from 10 is 10. The number of ways of selecting the second team from the remaining 9 teams is 9.

Theorem: The fundamental principle of counting: If event E can occur n different ways, and event F can occur m different ways, then the total number of outcomes is

n \times m

.

So,

10 \times 9

However, choosing team A then team B, is the same as choosing team B and then team A. So you have double counted. i.e. you have put in order, when there is no order.

So divide by