# how many different outcomes question

• Sep 25th 2006, 10:55 PM
catskill
how many different outcomes question
I want to find out all the different combinations of 16 different sets, for example here is what my set looks like

a-b
a-b

for just two sets i figure there are 4 different outcomes

outcome 1.
a-b
a-b

outcome 2.
b-a
b-a

outcome 3.
b-a
a-b

outcome 4.
a-b
b-a
which would be 2 x 2 =4, and if its 4 sets
a-b
a-b
a-b
a-b
I get 16 different outcomes 4 x 4=16
but for 16 sets I would think it would just be 16 X 16=256
but when writing out all the possible outcomes it seems like it would be more than that. What would be a good formula to figure out all the different outcomes or even what would the answer be, thanks
• Sep 27th 2006, 06:13 AM
Soroban
Hello, catskill!

If no one is responding, it's because we can't figure out what you're saying . . .

Quote:

I want to find out all the different combinations of 16 different sets.
Exactly how are these "combinations" formed?
It seems that we have 16 objects.
Are we taking them one at a time, then two at a time, then three at a time, etc. ?

For example here is what my set looks like:

a-b
a-b
Just what is this set?
Are there two objects in the set ... both of them "a-b"?
Is that really a subtraction?

We might be able to help if you gave us the original problem.

• Sep 27th 2006, 02:26 PM
catskill
Sorry, looking at it now it does look confusing, I was trying to turn a outcome issue into a math type question and probably confused things. Here my original question.

Their are 14 games football games played on sunday
ex.
CARDINALS vs FALCONS
VIKINGS vs BILLS
SAINTS vs PANTHERS
COLTS vs JETS
49ERS vs CHIEFS
COWBOYS vs TITANS
CHARGERS vs RAVENS
DOLPHINS vs TEXANS
LIONS vs RAMS
PATRIOTS vs BENGALS
BROWNS vs RAIDERS
REDSKINS vsSEAHAWKS
PACKERS vs EAGLES
patriots vs broncos

I have a pool at work where you pick all the winners for the week, i just wanted to know how many different outcomes their are and how i can find this out. If it was 3 games i get 9 different outcomes but for 14, i thought i would just multiply 14 by 14 and get 196 different outcomes but i think their are even more. What way can i get this answer, thanks.
• Sep 27th 2006, 03:01 PM
Plato
Just consider your first three examples.
CARDINALS vs FALCONS
VIKINGS vs BILLS
SAINTS vs PANTHERS
There are only eight possible outcomes not nine.
C V S
C V P
C B S
C B P
F V S
F V P
F B S
F B P
That is 2^3.
So with 14 matches there are 2^14 possible outcomes.
• Sep 27th 2006, 06:55 PM
catskill
Thanks, and by 2^14 u mean 2x2x2x2x2x2x2x2x2x2x2x2x2x2 right?
One more question
with these teams
bills vs lions
falcons vs saints
jags vs pats

and if their was 3 outcomes per game example
bills-win
lions-win
bills/lion-tie

how many different outcomes, for this i get 27 for all 3 games, is this right.