- Inicio
- Combinatorics
- Permutations with repetition
- Ejercicios
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?
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: $$P_{20}^{10,6,4}=\dfrac{20!}{10!6!4!}=38.798.760$$
$20$ girls can put themselves in line of $38.798.760$ different forms, if only the color of their hair is considered.