Task

Write a program that generates all   permutations   of   n   different objects.   (Practically numerals!)



Related tasks
 
   Find the missing permutation
   Permutations/Derangements



 The number of samples of size k from n objects.


With   combinations and permutations   generation tasks. 






 Order Unimportant

 Order Important


 Without replacement








(


n
k


)




=

n



C

k


=



n
(
n
−
1
)
…
(
n
−
k
+
1
)


k
(
k
−
1
)
…
1





{\displaystyle {\binom {n}{k}}=^{n}\operatorname {C} _{k}={\frac {n(n-1)\ldots (n-k+1)}{k(k-1)\dots 1}}}










n



P

k


=
n
⋅
(
n
−
1
)
⋅
(
n
−
2
)
⋯
(
n
−
k
+
1
)


{\displaystyle ^{n}\operatorname {P} _{k}=n\cdot (n-1)\cdot (n-2)\cdots (n-k+1)}




Task: Combinations

Task: Permutations


 With replacement








(



n
+
k
−
1

k


)




=

n
+
k
−
1



C

k


=



(
n
+
k
−
1
)
!


(
n
−
1
)
!
k
!





{\displaystyle {\binom {n+k-1}{k}}=^{n+k-1}\operatorname {C} _{k}={(n+k-1)! \over (n-1)!k!}}








n

k




{\displaystyle n^{k}}




Task: Combinations with repetitions

Task: Permutations with repetitions



list$ = "h,e,l,l,o"		' supply list seperated with comma's
 
while word$(list$,d+1,",") <> ""  'Count how many in the list
d = d + 1
wend
 
dim theList$(d)			' place list in array
for i = 1 to d
  theList$(i) = word$(list$,i,",")
next i
 
for i = 1 to d			' print the Permutations
 for j = 2 to d
   perm$ = ""
   for k = 1 to d
    perm$ = perm$ + theList$(k)
   next k
   if instr(perm2$,perm$+",") = 0 then print perm$ ' only list 1 time
   perm2$ 	 = perm2$ + perm$ + ","
   h$		 = theList$(j)
   theList$(j)	 = theList$(j - 1)
   theList$(j - 1) = h$
  next j
next i
end