Problems from Permutations with repetition

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?

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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: $P_{20}^{10, 6, 4} = \frac{20!}{10! 6! 4!} = 38.798 .760$

Solution:

$20$ girls can put themselves in line of $38.798 .760$ different forms, if only the color of their hair is considered.

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