Respuesta :
Answer:
a) 1820 ways
b) 43680 ways
Step-by-step explanation:
When the order of the choices is relevant we use the permutation formula:
[tex]P_{n,x}[/tex] is the number of different permutations of x objects from a set of n elements, given by the following formula.
[tex]P_{n,x} = \frac{n!}{(n-x)!}[/tex]
When the order of choices is not relevant we use 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 the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, we have that:
[tex]x = 4, n = 16[/tex]
(a) How many ways can this be done, if the order of the choices is not relevant?
[tex]C_{16,4} = \frac{16!}{4!(12)!} = 1820[/tex]
(b) How many ways can this be done, if the order of the choices is relevant?
[tex]P_{16,4} = \frac{16!}{(12)!} = 43680[/tex]
