All possible combos?

[Phoenix]

I'm trying to find all possible combos for a group of four letters (F, W, E, and A) into a group of three for my game. Mathematically, it should be 24, I think, but I only got 20. The order does not matter and the letters can be reused...

Here's the list of letter combos I have:

FFF
FFW
FFE
FFA
FWW
FWE
FWA
FEE
FEA
FAA
WWW
WWE
WWA
WEE
WEA
WAA
EEE
EEA
EAA
AAA

 

[Dalton]

Here is what I get and I think I missed two combos:

Spoiler

1.)FFF
2.)FFW
3.)FFE
4.)FFA
5.)FWF
6.)FWW
7.)FWE
8.)FWA
9.)FEF
10.)FEW
12.)FEA
13.)FEE
14.)FAF
15.)FAW
16.)FAA
17.)FAE
18.)WWW
19.)WWF
20.)WWA
21.)WWE
22.)WFW
23.)WFF
24.)WFA
25.)WFE
26.)WAW
27.)WAF
28.)WAA
29.)WAE
30.)AAA
31.)AAW
32.)AAF
33.)AAE
34.)AWW
35.)AWF
36.)AWA
37.)AWE
38.)AFW
39.)AFF
40.)AFE
41.)AFA
42.)AEW
43.)AEF
44.)AEE
45.)AEA
46.)EEE
47.)EEW
48.)EEF
49.)EEA
50.)EWW
51.)EWF
52.)EWE
53.)EWA
54.)EFW
55.)EFF
56.)EFE
57.)EFA
58.)EAW
59.)EAF
60.)EAE
62.)EAA

 

[Majal]

you missed 4 combos, and you also went from n° 10 to 12 and from 60 to 62, which explains why it looks like you only missed 2. There should be 64 combos: 4*4*4 options. You missed WEW, WEF, WEA and WEE.

 

[Dalton]

Ah thank you, didn't notice that. I thought it should be 64 as well.
I did kind of in a hurry so: my mistake. But now you have all the combos Phoenix.

Little question though: How did you get 24 as a result?

 

[regi]

He said the order doesn't matter, so as an example, FFW, FWF, and WFF would all count as the same combination.
Are you sure you're doing the math correctly? I got 20 as well.

 

[Dalton]

Ah, I didn't see that order doesn't matter.
Then you are right. 20 should be the solution.
Which means I did this for nothing. It was fun though.

 

[Brewmeister]

The number of combinations with repetition can be calculated as:
http://upload.wikimedia.org/math/6/f/e/ ... 03801e.png[/img]

(4 + 3 - 1)! / 3!(4-1)!  =  6! / 3!(3!)  =  720 / 36  =  20