Respuesta :

irspow
Since order is not important for unique combinations, we need to apply the "n choose k" formula....

n!/(k!(n-k)!), n=number of elements to choose from, k=number of choices made

In this case:

8!/(3!(8-3)!)

56

So there are 56 unique threesomes possible with 8 members.

There are total 56 ways to fill the open spot .

What is combination?

A combination is a way for determining the number of possible arrangements in a collection of items where the order of selection does not matter.

Formula for combination

[tex]C(n, r) =\frac{n!}{(n - r)!r!}[/tex]

where,

n is the number of items in set.

r is the number of items selected from the set.

According to the question we have,

Number of altos, n = 8

Number of  open spots, r = 3

Therefore, the number of ways to fill open spots = C(8, r)

Number of ways = [tex]\frac{8!}{3!(8-3)!}[/tex]

Number of ways = [tex]\frac{8!}{5!3!}[/tex][tex]= \frac{(8)(7)(6)(5!)}{5!3!}[/tex] = [tex]\frac{(8)(7)(6)}{(3)(2)} =8(7) = 56[/tex]

Hence, there are total 56 ways to fill the open spot .

Learn more about the combination here:

https://brainly.com/question/11709346

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