I have 40 participants competing in a contest. In that contest, we have a fixed number of Tables, and each Contestant's entry could land on any of those tables. For purposes of this discussion, let's say we have a total of 7 tables.

The maximum number of entries allowed on a table is 6. The minimum is 3. Entries are allocated as evenly as possible across those tables, although some will always have more than others in this example. For example:

Table 1 - 6 entries

Table 2 - 6 entries

Table 3 - 6 entries

Table 4 - 6 entries

Table 5 - 6 entries

Table 6 - 5 entries

Table 7 - 5 entries

For this discussion, the number of tables will never increase or decrease, and the number of entries will never increase or decrease. The "entry counts" on each table are irrelevant - for example, it does not matter if Table 1 has 5 entries, or if Table 2 has 5 entries, so long as the total number of entries for all tables is exactly 40.

Is there an equation I can use to determine the odds of exact duplication of entries landing on each table? For example if Teams 1, 2, 3, 4, 5 and 6 all land on Table 1, what are the odds of that recurring?

Also, is there an equation that would determine the odds of exact duplication for all tables and entries?

The number of possible arrangements is 40!/[(6!^5)*(5!^2)] = 2.928 x 10^29