19 ladies are there in a group. Find the number of ways, in which they can be made to stand in 2 circles of 9 and 10 ladies?

We need to SELECT people.
[SELECT = Combination = ⁿC_r = n!/r!(n-r)!

Here, we first have to select 10 ladies from 19.
Select = Combination
∴ Select 10 ladies = ¹⁹C₁₀

Arrange 10 ladies in circle = 10 - 1 = 9! ways
19 - 10 = 9 ladies remain.
Arrange the remaining 9 ladies in another circle = 9 - 1 = 8! ways

∴ Total ways to arrange 19 ladies in 2 required circles = ¹⁹C₁₀ × 9! × 8!