LAMBDA Halloween Challenge

Patrick2788 

Finally, I have a solution!

This time I used a Lambda function to add 1 to the previous index (stored in base n) but before returning the value, I scanned the digits and copied the larger digit across.

WorksheetFormula
= LET(
      count, COUNTA(Items),
      initialise, REPT("0",pick),
      indices, VSTACK(
               initialise, 
               SCAN(initialise, SEQUENCE(combinations-1), NextCombinationλ(count,pick))
               ),
      INDEX(Items, 1 + Explodeλ(indices))
   )

where

NextCombinationλ
= LAMBDA(n,p, 
     LAMBDA(initial,s,
        LET(
            place,     n^SEQUENCE(1,p,p-1,-1),
            increment, 1 + SUM(place * Explodeλ(initial)),
            converted, BASE(increment,n,p),
            vector,    Explodeλ(converted),
            modified,  SCAN( , vector, Maxλ),
            CONCAT(modified)
        )
     )
  );

supported by

Explodeλ = LAMBDA(term, MID(term, SEQUENCE(1,pick), 1));

Maxλ = LAMBDA(u, v, Max(u,v));

I have just performed the calculation for 8 picks taken for 9 items in 300ms.  Ther are 12,870 combinations and the permutations would have been over 43M!