There are

ways to pick 5 people from the group of 10. Then there are

ways to arrange each group around the table.

Normally we would have to consider the double counting case.

Suppose the 10 people are named A, B, C … J.

Using

to pick five people means that picking

is counted separately to picking

, even though the same people are put in the same group each time.

However, in this case, since the tables are distinct, the order of the groups actually does matter, i.e.

is different to

.

Possibly a less confusing way to think about it is:

gives the number of distinct ways in which 10 people can be divided into two groups.

Each group of 5 can be arranged around the table in

ways.

And there are

ways to assign each group of 5 to a table, since the tables are distinct.

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