i think the answer is 122,400
Answer:
Hello,
Step-by-step explanation:
0 girls and 8 boys :
![\left(\begin{array}{c}10\\ 8\end{array}\right)=10*9*8*7*6*5*4*3/8!=45\\\\](https://tex.z-dn.net/?f=%5Cleft%28%5Cbegin%7Barray%7D%7Bc%7D10%5C%5C%208%5Cend%7Barray%7D%5Cright%29%3D10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2F8%21%3D45%5C%5C%5C%5C)
1 girl and 7 boys:
![\left(\begin{array}{c}6\\ 1\end{array}\right)*\left(\begin{array}{c}10\\7\end{array}\right)=6*10*9*...*4/7!=6*120=720\\\\](https://tex.z-dn.net/?f=%5Cleft%28%5Cbegin%7Barray%7D%7Bc%7D6%5C%5C%201%5Cend%7Barray%7D%5Cright%29%2A%5Cleft%28%5Cbegin%7Barray%7D%7Bc%7D10%5C%5C7%5Cend%7Barray%7D%5Cright%29%3D6%2A10%2A9%2A...%2A4%2F7%21%3D6%2A120%3D720%5C%5C%5C%5C)
2 girl and 6 boys:
![\left(\begin{array}{c}6\\ 2\end{array}\right)*\left(\begin{array}{c}10\\6\end{array}\right)=60*210=1260\\](https://tex.z-dn.net/?f=%5Cleft%28%5Cbegin%7Barray%7D%7Bc%7D6%5C%5C%202%5Cend%7Barray%7D%5Cright%29%2A%5Cleft%28%5Cbegin%7Barray%7D%7Bc%7D10%5C%5C6%5Cend%7Barray%7D%5Cright%29%3D60%2A210%3D1260%5C%5C)
3 girl and 5 boys:
![\left(\begin{array}{c}6\\ 3\end{array}\right)*\left(\begin{array}{c}10\\5\end{array}\right)\\](https://tex.z-dn.net/?f=%5Cleft%28%5Cbegin%7Barray%7D%7Bc%7D6%5C%5C%203%5Cend%7Barray%7D%5Cright%29%2A%5Cleft%28%5Cbegin%7Barray%7D%7Bc%7D10%5C%5C5%5Cend%7Barray%7D%5Cright%29%5C%5C)
4 girls and 4 boys:
![\left(\begin{array}{c}6\\ 4\end{array}\right)*\left(\begin{array}{c}10\\4\end{array}\right)](https://tex.z-dn.net/?f=%5Cleft%28%5Cbegin%7Barray%7D%7Bc%7D6%5C%5C%204%5Cend%7Barray%7D%5Cright%29%2A%5Cleft%28%5Cbegin%7Barray%7D%7Bc%7D10%5C%5C4%5Cend%7Barray%7D%5Cright%29)
5 girls and 3 bys:
![\left(\begin{array}{c}6\\ 5\end{array}\right)*\left(\begin{array}{c}10\\3\end{array}\right)](https://tex.z-dn.net/?f=%5Cleft%28%5Cbegin%7Barray%7D%7Bc%7D6%5C%5C%205%5Cend%7Barray%7D%5Cright%29%2A%5Cleft%28%5Cbegin%7Barray%7D%7Bc%7D10%5C%5C3%5Cend%7Barray%7D%5Cright%29)
I let you to calculate and make the sum.
Answer:
-13/84
Step-by-step explanation:
Calculation to Find the exact value of the trigonometric expression
First step is to find tan(u)
Based on the information given we were told that sin(u) = -3/5 which means if will have -3/5 in the 4th quadrant would have triangle 3-4-5
Hence:
tan(u)=-3/4
Second step is to calculate tan(v)
In a situation where cos(v) is 15/17 which means that we would have triangle 8-15-17
Hence:
tan(v) = 8/15
Now Find the exact value of the trigonometric expression using this formula
tan(u+v) = (tan(u) + tan(v))/(1-tan(u)tan(v)
Where,
tan(u)=-3/4
tan(v)=8/15
Let plug in the formula
tan(u+v)=(-3/4)+(8/15)÷[1-(-3/4)(8/15]
tan(u+v)=(-45+32)÷(60-24)
tan(u+v)=-13/84
Therefore exact value of the trigonometric expression will be -13/84