Four-letter words that can be formed from the letters of the word "facetious" without letter duplication

Question

How do I construct all four-letter words from the letters of "facetious," without duplicating letters?

Answer 1

The total number of possibilities is $9\times 8\times 7\times 6=3024$ If you need real words, this is beyond the scope of this forum. You need to consult a dictionary.

Answer 2

I think it's safe to assume your math class isn't setting English word assignments.

There are $\frac{9!}{4!5!} = 126$ unique $4$ letter combinations

For every $4$ letter combination, it can be arranged in $4! = 24$ ways. This is a total number of permutations of $4$ from $9$ of $126\cdot 24 = 3024$.

Another way is simply $\frac{9!}{5!} = 3024$

Answer 3

There are 61 valid English words with your constraints:

{"aces", "acts", "ates", "auto", "cafe", "case", "cast", "cats", 
"ciao", "cite", "cits", "coat", "coif", "cost", "cote", "cots", 
"cues", "cute", "cuts", "east", "eats", "ecus", "etas", "face", 
"fact", "fast", "fate", "fats", "feat", "fest", "feta", "fiat", 
"fies", "fist", "fits", "foes", "fuse", "ices", "iota", "oafs", 
"oats", "oust", "outs", "safe", "sate", "scat", "seat", "sect", 
"sift", "site", "sofa", "soft", "suet", "suit", "taco", "taus", 
"teas", "tics", "ties", "toes", "tofu"}

In Mathematica:

Select[
     DictionaryLookup[___], 
       ContainsOnly[Characters[#], Characters["facetious"]] && 
       DuplicateFreeQ[Characters[#]] && 
       StringLength[#] == 4 &]

I presume @Misah Lavrov used similar code, above.