Final answer:
The business man can arrange the guests in a total of 82,616 ways.
Step-by-step explanation:
To arrange the guests, we need to consider two scenarios: Scenario 1 - all guests fit on the first table, and Scenario 2 - some guests need to sit at the second table.
In Scenario 1, all 21 guests can fit on the first table, which can accommodate 15 people. Therefore, we need to choose 15 guests out of 21 to sit on the first table. This can be done in C(21, 15) = 68,860 ways.
In Scenario 2, some guests need to sit at the second table. Let's say 'x' guests sit on the first table and '21-x' guests sit on the second table. The number of ways to arrange 'x' guests on the first table is C(15, x), and the number of ways to arrange '21-x' guests on the second table is C(6, 21-x). To calculate the total number of arrangements, we need to sum up the arrangements for each value of 'x' from 0 to 15. This can be expressed as:
∑x=015 C(15, x) * C(6, 21-x)
Calculating this sum gives us a total of 13,756 ways to arrange the guests in Scenario 2.
Therefore, the total number of ways to arrange the guests is the sum of the arrangements from both scenarios: 68,860 + 13,756 = 82,616 ways.