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

Sagot :

caylus

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.

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