If all the females are seated together, we can treat them as a single group. This means that we have 16 entities (the group of females and the 15 males) to arrange around the round table.
The number of ways to arrange 16 entities in a round table is (16-1)! = 15!, because we fix one person's position and then arrange the rest around the table. However, within the group of females, they can also arrange themselves, which is 10! since there are 10 females.
So, the total number of ways they can be seated with all the females together is 15! * 10!.
Let's calculate this:
15! = 1,307,674,368,000 10! = 3,628,800
Total ways = 1,307,674,368,000 * 3,628,800 ≈ 4.7425 × 10^18
There are approximately 4.7425 × 10^18 ways they can be seated if all the females are seated together.