Respuesta :
Using the combination and the permutation formula, we have that there are:
a) 2970 ways.
b) 11880 ways.
If the order is not important, the combination formula is used:
Combination formula:
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]
If the order is important, the permutation formula is used:
Permutation formula:
The number of possible permutations of x elements from a set of n elements is given by:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
Item a:
- Order does not matter, so combination.
- 8 from a set of 10 at the windows.
- 2 from a set of 12 at the remaining places.
Thus:
[tex]C_{10,8}C_{12,2} = \frac{10!}{2!8!} \times \frac{12!}{2!10!} = 2970[/tex]
2970 ways.
Item b:
- Order matters, so permutations.
- 8 from a set of 10 at the windows.
- 2 from a set of 12 at the remaining places.
Thus:
[tex]P_{10,8}P_{12,2} = \frac{10!}{8!} \times \frac{12!}{10!} = 11880[/tex]
11880 ways.
A similar problem is given at https://brainly.com/question/25167740
