Answer:
Hello,
Step-by-step explanation:
0 girls and 8 boys :
[tex]\left(\begin{array}{c}10\\ 8\end{array}\right)=10*9*8*7*6*5*4*3/8!=45\\\\[/tex]
1 girl and 7 boys:
[tex]\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\\\\[/tex]
2 girl and 6 boys:
[tex]\left(\begin{array}{c}6\\ 2\end{array}\right)*\left(\begin{array}{c}10\\6\end{array}\right)=60*210=1260\\[/tex]
3 girl and 5 boys:
[tex]\left(\begin{array}{c}6\\ 3\end{array}\right)*\left(\begin{array}{c}10\\5\end{array}\right)\\[/tex]
4 girls and 4 boys:
[tex]\left(\begin{array}{c}6\\ 4\end{array}\right)*\left(\begin{array}{c}10\\4\end{array}\right)[/tex]
5 girls and 3 bys:
[tex]\left(\begin{array}{c}6\\ 5\end{array}\right)*\left(\begin{array}{c}10\\3\end{array}\right)[/tex]
I let you to calculate and make the sum.
