Answer:
7 available
Explanation:
Since 3 colors are available r = 3
Total combination = 35
nCr = 35 ---1
nCr = n!/(n-r)!r!---2
We put equation 1 and 2 together
n-1)(n-2)(n-3)!/n-3)! = 35x 3!
We cancel out (n-3)!
(n-1)(n-2) = 210
7x6x5 = 210
nC3 = 35
7C3 = 35
So If there are 35 combinations, 7 colors are available.
Thank you!
The available colors are illustrations of combination, and there are 7 colors available.
The given parameters are:
[tex]Total = 35[/tex] --- the number of combinations
[tex]r = 3[/tex] -- the number of colors in one combination.
The number of combinations is calculated using:
[tex]Total = ^nC_r[/tex]
Where n represents the number of colors available.
So, we have:
[tex]35= ^nC_3[/tex]
Apply combination formula
[tex]35= \frac{n!}{(n - 3)!3!}[/tex]
Expand the numerator
[tex]35= \frac{n(n - 1)(n - 2)(n - 3)!}{(n - 3)!3!}[/tex]
Cancel out the common factors
[tex]35= \frac{n(n - 1)(n - 2)}{3!}[/tex]
Expand
[tex]35= \frac{n(n - 1)(n - 2)}{3 \times 2 \times 1}[/tex]
[tex]35= \frac{n(n - 1)(n - 2)}{6}[/tex]
Multiply both sides by 6
[tex]210= n(n - 1)(n - 2)[/tex]
Rewrite the equation as
[tex]n(n - 1)(n - 2) = 210[/tex]
Using a graphing calculator, we have:
[tex]n = 7[/tex]
Hence, the number of colors available is 7
Read more about combination at:
https://brainly.com/question/4519122
