Final answer:
There are 5040 possible orders that the seven guests can arrive in.
Step-by-step explanation:
To calculate the number of possible orders that the seven guests can arrive in, we can use the concept of permutations.
Since each guest has a distinct order they can arrive in, we need to find the number of permutations of seven guests.
The formula for permutations is P(n, r) = n! / (n - r)!, where n is the total number of elements and r is the number of elements taken at a time.
In this case, n is 7 and r is also 7, so the calculation would be:
P(7, 7) = 7! / (7 - 7)! = 7! / 0!
= 7!
= 7 x 6 x 5 x 4 x 3 x 2 x 1
= 5040.
Therefore, there are 5040 possible orders that the seven guests can arrive in.