Question

A table tennis tournament is to be round-robin; that is, each player plays one match against every other player. How many matches will be played if 5 people enter the tournament?

Answer 1

\(\bf \Large \cfrac{n!}{(n-r)!}\)

n = total number
r = group off the total number

Answer 2

Group off the total number?

Answer 3

yes, you have 5 players total
"each player plays one match against every other player"

so 2 players are playing against each other, that is 2 at a time off a total of 5 folks
no repetition

Answer 4

ok but then what do you mean by "total number"?

Answer 5

is a permutation matter, so you'd have a total number, from where a fraction is used for the mixing

Answer 6

Could you please give me a smaller example of this problem and solve it using this exact same strategy? Thank you so much if you could!

Answer 7

say you go to the local ice cream store to get a milk shake
you like your milk shake of 2 flavors

the store has 10 different flavors

in how many ways can the store meet your taste of 2 flavors for the milk shake?

from 10 flavors, they'd have to combine 2 flavors for your milk shake
so total flavors is 10
fragment to be used for mixing, is 2
\(\bf \cfrac{n!}{(n-r)!} \implies \cfrac{10!}{(10-2)!} \implies \cfrac{3628800}{40320} = 90\)

so they can combine 2 flavors for you off their 10 flavors they have
in 90 different ways

Answer 8

Wow! Thank you so, so much for your help!!!!! :)

Answer 9

yw