In a group of $$20$$ girls there are $$10$$ brunettes, $$6$$ blondes and $$4$$ redheads. In how many possible ways can they put themselves in line, bearing in mind only the color of their hair?
See development and solution
Development:
In this case $$n=20$$, since there are $$20$$ girls. There are three different classes of girl: brunettes $$(0)$$, blondes $$(6)$$ and redheads $$(4)$$. And so, we have that $$n_1=10$$, $$n_2=6$$ and $$n_3=4$$. Therefore, the permutations with repetition correspondents are: $$$P_{20}^{10,6,4}=\dfrac{20!}{10!6!4!}=38.798.760$$$
Solution:
$$20$$ girls can put themselves in line of $$38.798.760$$ different forms, if only the color of their hair is considered.