Task

Given non-negative integers    m    and    n,   generate all size    m    combinations   of the integers from    0   (zero)   to    n-1    in sorted order   (each combination is sorted and the entire table is sorted).



Example

3   comb    5      is:

0 1 2
0 1 3
0 1 4
0 2 3
0 2 4
0 3 4
1 2 3
1 2 4
1 3 4
2 3 4

If it is more "natural" in your language to start counting from    1   (unity) instead of    0   (zero),

the combinations can be of the integers from    1   to    n. 



See also


 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



 
Module Checkit {
      Global a$
      Document a$
      Module Combinations (m as long, n as long){
            Module Level (n, s, h)   {
                  If n=1 then {
                        while Len(s) {
                               Print h, car(s)
                               ToClipBoard()
                               s=cdr(s)
                         }
                  } Else {
                        While len(s) {
                              call Level n-1, cdr(s),  cons(h, car(s))
                              s=cdr(s)
                        }  
                  }
                  Sub ToClipBoard()
                        local m=each(h)
                        Local b$=""
                        While m {
                              b$+=If$(Len(b$)<>0->" ","")+Format$("{0::-10}",Array(m))
                        }
                        b$+=If$(Len(b$)<>0->" ","")+Format$("{0::-10}",Array(s,0))+{
                        }
                        a$<=b$   ' assign to global need <=
                  End Sub
            }
            If m<1 or n<1 then Error 
            s=(,)
            for i=0 to n-1 {
                  s=cons(s, (i,))
            }
            Head=(,)
            Call Level m,  s, Head
      }
      Clear a$
      Combinations 3, 5
      ClipBoard a$
}
Checkit
 