A class has 10 boys and 12 girls. In how many ways can a committee of four be selected if the committe can have at most two girls?

Please show formulas.

Thanks,

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- May 17th 2006, 12:14 PMgogo08combinatorics
A class has 10 boys and 12 girls. In how many ways can a committee of four be selected if the committe can have at most two girls?

Please show formulas.

Thanks, - May 21st 2006, 09:21 AMThePerfectHackerQuote:

Originally Posted by**gogo08**

0 Girls

1 Girl

2 Girls

In each case respectively we have,

$\displaystyle _{10}C_4 \cdot _{12}C_0=210$

$\displaystyle _{10}C_3 \cdot _{12}C_1=1440$

$\displaystyle _{10}C_2 \cdot _{12}C_2=2970$

In total,

4260