Answer :
Answer:
210
Step-by-step explanation:
10x9x8x7x6x5x4x3x2x1 divided by 6x5x4x3x2x1x4x3x2x1=
(Take out 1 through 6 on both sides)
10x9x8x7 divided by 4x3x2x1=
5040 divided by 24=
210
Dance instructor can chose 4 students out of 10 if order doesn't matter in 210 ways
What is combination?
A combination is a selection of all or part of a set of objects, without regard to the order in which objects are selected.
For example, suppose we have a set of three letters: A, B, and C. We might ask how many ways we can select 2 letters from that set. Each possible selection would be an example of a combination.
Formula of combination:
[tex]C_{n} ^{r} = \frac{n!}{r! (n-r)!}[/tex]
Where
nCr is the selection of objects from a group of objects where order of objects does not matter.
n is the total number of objects
r is the number of selected objects.
According to the question
A dance instructor chose four of his 10 students to be on stage for a performance and order does not matter .
i.e,
if we have to chose and order does not matter that means we have to use combination .
[tex]C_{n} ^{r} = \frac{n!}{r! (n-r)!}[/tex]
Total number of students (n)= 10
Number of selected students (r) = 4
[tex]C_{n} ^{r} = \frac{n!}{r! (n-r)!}[/tex]
[tex]C_{n} ^{r} = \frac{10!}{4! (6)!}[/tex]
[tex]C_{n} ^{r} = \frac{10*9*8*7}{4*3*2*1 }[/tex]
[tex]C_{n} ^{r} = \frac{5040}{24 }\\[/tex]
[tex]C_{n} ^{r} = 210[/tex]
Hence, Dance instructor can chose 4 students out of 10 in 210 ways
To know more about combination here :
https://brainly.com/question/27014146
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