Respuesta :
Using the combination and the arrangements formula, it is found that the number of possible playlists is given by:
[tex]7.98 \times 10^8[/tex]
What is the combination formula?
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, we have that:
- 7 disco songs are taken from a set of 7.
- 3 remaining songs are taken from a set of 3 + 6 + 3 = 12 songs.
Hence, without considering the order, the number of playlists is given by:
[tex]C_{7,7}C_{12,3} = \frac{7!}{7!0!} \times \frac{12!}{3!9!} = 220[/tex]
What is the arrangements formula?
The number of possible arrangements of n elements is given by the factorial of n, that is:
[tex]A_n = n![/tex]
In this problem, the 10 musics are arranged, hence the number of playlists, considering the order, is given by:
[tex]n = 10! \times 220 = 798336000 = 7.98 \times 10^8[/tex]
More can be learned about the combination formula at https://brainly.com/question/25821700
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