# How many possible combinations of 5 are there in 12

1. Nov 11, 2009

### justasimplegy

hello.i need some help.i need to know how many possible combinations of 5(abcde etc.) are there in 12( abcdefghijkl)eg.their are 12 games of hockey that can end in a tie(shootout).each game is designated as a,b,c,d,e,f,g,h,i,j,k,l. 5 of the games will be tied.i need to know how many possible combinations there will be.thanks.....ken...

2. Nov 11, 2009

### pbandjay

I think I am confused. Are you just asking how many ways are there to pick five games out of 12? If so then I think you may be looking for

$$\binom{12}{5}=792$$

Or is there more of a stipulation on whether a game can end in a tie?

3. Nov 16, 2009

### justasimplegy

thanks and hello.i mean there are 12 games.lets just say a,b,c,d,e,f,g,h,i,j,k,l, .eg: so games a.c.d.j.k.ends in ties.that means i have one right.i am looking for how many possible combinations there are in 12 games that i have to at least guess 5 correct.any groups of 5 ( eg: a,b,c,d,e ,f,g,h,k,l ,c,f,h,j,k etc. we have in vancouver a lottery for sports betting.if you can pick almost 5 hockey games that will end in ties(shootouts) and you bet 200 dollars,you will win almost 1 million.its hard to pick 5 on the nose but to pick 12 games that have the most chance of ending in ties is better odds for me.usually if i pick 12 games i get usually 6-8 correct in ties.other times its just 5.i want to know how many tickets i will have to buy to cover all the possible combos of the 12 games.they have to be 5 correct in any way.if its 792 combos that would mean it would cost me 158,400 dollars.but if i get all 12 correct i will win close to 792 million.i would risk my house to bet that much as i am tired of working.thanks for help.one friend said it would be higher than 792.this might help explain where im coming from.5 games out of 6 games played the possible combo is 6.thanks..ken

4. Nov 19, 2009

### zgozvrm

pbandjay is right, if I understand your question correctly. To summarize, your question reads: How many combinations of 5 games are there, given that there are 12 games to be played?

This would mean that order has no significance (abcde is the same as edcba is the same as baedc, etc.). Therefore, we're talking about combinations, not permutations and 792 is the answer. If order was significant, then you'd be looking at 95,040 possibilities.

5. Nov 20, 2009

### justasimplegy

thanks for the speedy reply.yes 792 would be it as it doesnt have to be in any order just as long as i have 5 correct out of the 12 games played.if and when i do buy my tickets and i win.i will remember those of you who helped.\$...thanks.ken