Question

There are 10 boys and 6 girls. How many ways are there to choose 8 people to get at most 5 girls

Answer 1

Hello,

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\\\\`

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\\\\`

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\\`

3 girl and 5 boys:

`\left(\begin{array}{c}6\\ 3\end{array}\right)*\left(\begin{array}{c}10\\5\end{array}\right)\\`

4 girls and 4 boys:

`\left(\begin{array}{c}6\\ 4\end{array}\right)*\left(\begin{array}{c}10\\4\end{array}\right)`

5 girls and 3 bys:

`\left(\begin{array}{c}6\\ 5\end{array}\right)*\left(\begin{array}{c}10\\3\end{array}\right)`

I let you to calculate and make the sum.