maths help for an idiot

Punchbowl4

right guys, i need some help. much appreciated if somebody can answer me this.

lets say there are 5 football matches. what i want to know, is how many combinations are there if i need there to be 2 home wins, 1 draw, and two away wins. i know this should be really simple, bit i'm a bit thick.
thanks

Fremen

An equivalent problem is how many different ways are there of arranging the letters h,h,a,a,d.

Imagine five empty "boxes". We'll pick one letter at a time and imagine ourselves writing it into a box.

Pick one of the h's first. We have five choices for which box to put it in.
Now for the second h. There are four boxes left, so pick one of them. That's five by four, which is twenty. However, if we switched the h's around, our arrangement would still look the same. This means there are actually half as many:

h,h,X,X,X

h,X,h,X,X

h,X,X,h,X

h,X,X,X,h

X,h,h,X,X

X,h,X,h,X

X,h,X,X,h

X,X,h,h,X

X,X,h,X,h

X,X,X,h,h

where X represents an empty box.
We have three choices left for a place to put the first 'a' now. Once we've done that, we have two choices to put the second a. Just like for the h's, we've double counted, so we need to divide by two. Once the h's and a's are in place, we only have one choice for where to put the d.
This gives a total of (5*4/2)*(3*2/2) = 30 possibilities.

Edit: there's no such thing as a maths idiot. It just takes a little practice.

Punchbowl4

many thanks, what part of probabilty would this fall under if i wanted to look into it further.

Fremen

It falls under permutations and combinations, which is a small part of a much larger branch of maths called combinatorics.

equivariant

Punchbowl4 wrote: »

many thanks, what part of probabilty would this fall under if i wanted to look into it further.

look up multinomial coefficients

nitrogen

Punchbowl4 wrote: »

many thanks, what part of probabilty would this fall under if i wanted to look into it further.

Khan Academy.

Gipo3

Thanks