Solution:
The permutation formula is expressed as
![\begin{gathered} P^n_r=\frac{n!}{(n-r)!} \\ \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20P%5En_r%3D%5Cfrac%7Bn%21%7D%7B%28n-r%29%21%7D%20%5C%5C%20%20%5Cend%7Bgathered%7D)
The combination formula is expressed as
![\begin{gathered} C^n_r=\frac{n!}{(n-r)!r!} \\ \\ \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20C%5En_r%3D%5Cfrac%7Bn%21%7D%7B%28n-r%29%21r%21%7D%20%5C%5C%20%20%5C%5C%20%20%5Cend%7Bgathered%7D)
where
![\begin{gathered} n\Rightarrow total\text{ number of objects} \\ r\Rightarrow number\text{ of object selected} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20n%5CRightarrow%20total%5Ctext%7B%20number%20of%20objects%7D%20%5C%5C%20r%5CRightarrow%20number%5Ctext%7B%20of%20object%20selected%7D%20%5Cend%7Bgathered%7D)
Given that 6 objects are taken at a time from 8, this implies that
![\begin{gathered} n=8 \\ r=6 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20n%3D8%20%5C%5C%20r%3D6%20%5Cend%7Bgathered%7D)
Thus,
Number of permuations:
![\begin{gathered} P^8_6=\frac{8!}{(8-6)!} \\ =\frac{8!}{2!}=\frac{8\times7\times6\times5\times4\times3\times2!}{2!} \\ 2!\text{ cancel out, thus we have} \\ \begin{equation*} 8\times7\times6\times5\times4\times3 \end{equation*} \\ \Rightarrow P_6^8=20160 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20P%5E8_6%3D%5Cfrac%7B8%21%7D%7B%288-6%29%21%7D%20%5C%5C%20%3D%5Cfrac%7B8%21%7D%7B2%21%7D%3D%5Cfrac%7B8%5Ctimes7%5Ctimes6%5Ctimes5%5Ctimes4%5Ctimes3%5Ctimes2%21%7D%7B2%21%7D%20%5C%5C%202%21%5Ctext%7B%20cancel%20out%2C%20thus%20we%20have%7D%20%5C%5C%20%5Cbegin%7Bequation%2A%7D%208%5Ctimes7%5Ctimes6%5Ctimes5%5Ctimes4%5Ctimes3%20%5Cend%7Bequation%2A%7D%20%5C%5C%20%5CRightarrow%20P_6%5E8%3D20160%20%5Cend%7Bgathered%7D)
Number of combinations:
![\begin{gathered} C^8_6=\frac{8!}{(8-6)!6!} \\ =\frac{8!}{2!\times6!}=\frac{8\times7\times6!}{6!\times2\times1} \\ 6!\text{ cancel out, thus we have} \\ \frac{8\times7}{2} \\ \Rightarrow C_6^8=28 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20C%5E8_6%3D%5Cfrac%7B8%21%7D%7B%288-6%29%216%21%7D%20%5C%5C%20%3D%5Cfrac%7B8%21%7D%7B2%21%5Ctimes6%21%7D%3D%5Cfrac%7B8%5Ctimes7%5Ctimes6%21%7D%7B6%21%5Ctimes2%5Ctimes1%7D%20%5C%5C%206%21%5Ctext%7B%20cancel%20out%2C%20thus%20we%20have%7D%20%5C%5C%20%5Cfrac%7B8%5Ctimes7%7D%7B2%7D%20%5C%5C%20%5CRightarrow%20C_6%5E8%3D28%20%5Cend%7Bgathered%7D)
Hence, there are 28 combinations and 20160 permutations.
Answer:
D
Step-by-step explanation:
Opposite sides of a parallelogram are congruent.
3x+ 2= 4x-3
Subtract 3x from both sides
2= x -3
Add 3 to both sides
5= x
2y+7=4y-9
Subtract 2y from both sides
7= 2y -9
Add 9 to both sides
16 = 2y
Divide by 2 on both sides
8 = y
The same line! hope this helps! i’m not 100% sure so if i’m wrong don’t flame me
When solving this equation, you get the answer as -43.5.
To solve, we simply need to collect like-terms and then rearrange to get x on one side and numbers on the other:
(8x - 20) - 16 = 10x + 51
8x - 36 = 10x + 51
- 8x
-36 = 2x + 51
- 51
-87 = 2x
÷ 2
-43.5 = x
I hope this helps!