# CombinatorialCase111

This case produces M-Tuples of N items. That is, all length M vectors with all possibilities of N items in each position, N*M rows all together.

• M labeled balls (1), N labeled boxes (1), any # balls per box (1)
• Sensitive to ⎕IO
• Allows Lexicographic order
• Counted result is an integer scalar
• Generated result is an integer matrix.

The count for this function is NM (↔ N*M).

For example:

If we have 2 labeled balls (❶❷) and 3 labeled boxes (123) with any # of balls per box, there are 9 (↔ 3*2) ways to meet these criteria:

 ❶❷ 1 2 3
 ❶ ❷ 1 2 3
 ❶ ❷ 1 2 3
 ❷ ❶ 1 2 3
 ❶❷ 1 2 3
 ❶ ❷ 1 2 3
 ❷ ❶ 1 2 3
 ❷ ❶ 1 2 3
 ❶❷ 1 2 3

The diagram above corresponds to

```      111 1‼2 3 ⍝ Tuples in unspecified order
1 1
1 2
1 3
2 1
2 2
2 3
3 1
3 2
3 3
111 2‼2 3 ⍝ Tuples in Lexicographic order
1 1
1 2
1 3
2 1
2 2
2 3
3 1
3 2
3 3
111 3‼2 3 ⍝ Gray Code order for Tuples not implemented as yet
NONCE ERROR
111 3‼2 3
∧
⍝ M-tuples of N items
⍝ Labeled balls & boxes, any # Balls per Box
111 0‼3 2
8
111 1‼3 2
1 1 1
1 1 2
1 2 1
1 2 2
2 1 1
2 1 2
2 2 1
2 2 2
```