(1) From the information given, if we want to choose 5 colors from 8 distinct colors and the order in which the selection is made is relevant, then what we have is a permutation.
The formula is given as;
![nP_r=\frac{n!}{(n-r)!}](https://tex.z-dn.net/?f=nP_r%3D%5Cfrac%7Bn%21%7D%7B%28n-r%29%21%7D)
This formula means we need to select/arrange r items out of a total of n items and the anwer derived would be the total number of arrangements possible.
Therefore, we would have;
![\begin{gathered} nP_r\Rightarrow_8P_5 \\ _8P_5=\frac{8!}{(8-5)!}\Rightarrow\frac{8!}{3!} \\ _8P_5=\frac{8\times7\times6\times\ldots1}{3\times2\times1}\Rightarrow\frac{40320}{6} \\ _8P_5=6720 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20nP_r%5CRightarrow_8P_5%20%5C%5C%20_8P_5%3D%5Cfrac%7B8%21%7D%7B%288-5%29%21%7D%5CRightarrow%5Cfrac%7B8%21%7D%7B3%21%7D%20%5C%5C%20_8P_5%3D%5Cfrac%7B8%5Ctimes7%5Ctimes6%5Ctimes%5Cldots1%7D%7B3%5Ctimes2%5Ctimes1%7D%5CRightarrow%5Cfrac%7B40320%7D%7B6%7D%20%5C%5C%20_8P_5%3D6720%20%5Cend%7Bgathered%7D)
Therefore, if the order is relevant, this selection can be done in 6,720 ways.
(2) If the order is NOT relevant, then what we need to calculate is a combination and the formula is;
![_nC_r=\frac{n!}{(n-r)!r!}](https://tex.z-dn.net/?f=_nC_r%3D%5Cfrac%7Bn%21%7D%7B%28n-r%29%21r%21%7D)
The formula can now be applied as follows;
![\begin{gathered} _nC_r\Rightarrow_8C_5 \\ _8C_5=\frac{8!}{(8-5)!\times5!} \\ _8C_5=\frac{8!}{3!\times5!}\Rightarrow\frac{8\times7\times6\times\ldots1}{(3\times2\times1)\times(5\times4\times\ldots1)} \\ _8C_5=\frac{40320}{6\times120} \\ _8C_5=56 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20_nC_r%5CRightarrow_8C_5%20%5C%5C%20_8C_5%3D%5Cfrac%7B8%21%7D%7B%288-5%29%21%5Ctimes5%21%7D%20%5C%5C%20_8C_5%3D%5Cfrac%7B8%21%7D%7B3%21%5Ctimes5%21%7D%5CRightarrow%5Cfrac%7B8%5Ctimes7%5Ctimes6%5Ctimes%5Cldots1%7D%7B%283%5Ctimes2%5Ctimes1%29%5Ctimes%285%5Ctimes4%5Ctimes%5Cldots1%29%7D%20%5C%5C%20_8C_5%3D%5Cfrac%7B40320%7D%7B6%5Ctimes120%7D%20%5C%5C%20_8C_5%3D56%20%5Cend%7Bgathered%7D)
If the order is not relevant, then the selection can be done in 56 ways.
207-180=27
27/180=0.15
The price of the a tablet increased by 15%
Answer:
<h3>
![\huge{ \boxed{ \bold{ \tt{10x - 5}}}}](https://tex.z-dn.net/?f=%20%5Chuge%7B%20%5Cboxed%7B%20%5Cbold%7B%20%5Ctt%7B10x%20-%205%7D%7D%7D%7D)
</h3>
♨ ![\text{Question} : \text{Simplify}](https://tex.z-dn.net/?f=%20%5Ctext%7B%3C%2Fstrong%3E%3Cstrong%3EQ%3C%2Fstrong%3E%3Cstrong%3Euestion%7D%20%3A%20%20%5Ctext%7B%3C%2Fstrong%3E%3Cstrong%3ESi%3C%2Fstrong%3E%3Cstrong%3Emplify%7D)
♨ ![\underbrace{ \text{Required \: Answer : } }](https://tex.z-dn.net/?f=%5Cunderbrace%7B%20%5Ctext%7BRequired%20%5C%3A%20Answer%20%3A%20%7D%20%7D)
First , combine like terms :
Like terms are those which have the same base.
![\longrightarrow{ \sf{ - 5x + 7x + 8x + 15 - 20}}](https://tex.z-dn.net/?f=%20%5Clongrightarrow%7B%20%5Csf%7B%20-%205x%20%2B%207x%20%2B%208x%20%2B%2015%20-%2020%7D%7D)
![\longrightarrow{ \sf{2x + 8x + 15 - 20}}](https://tex.z-dn.net/?f=%20%5Clongrightarrow%7B%20%5Csf%7B2x%20%2B%208x%20%2B%2015%20-%2020%7D%7D)
![\longrightarrow{ \sf{10x + 15 - 20}}](https://tex.z-dn.net/?f=%20%5Clongrightarrow%7B%20%5Csf%7B10x%20%2B%2015%20-%2020%7D%7D)
Remember : The negative and positive numbers are always subtracted but posses the sign of bigger integer.
![\longrightarrow{ \boxed{ \bold{ \text{10x - 5}}}}](https://tex.z-dn.net/?f=%20%5Clongrightarrow%7B%20%5Cboxed%7B%20%5Cbold%7B%20%5Ctext%7B10x%20-%205%7D%7D%7D%7D)
And we're done!
Hope I helped!
Best regards ! シ
~TheAnimeGirl
<h3>
Answer: C) 2</h3>
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Work Shown:
cot(theta) = cos(theta)/sin(theta)
cot(theta) = x/y
cot(theta) = -4/(-2)
cot(theta) = 2