# combinatorics

• May 17th 2006, 12:14 PM
gogo08
combinatorics
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?

Thanks,
• May 21st 2006, 09:21 AM
ThePerfectHacker
Quote:

Originally Posted by gogo08
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?

Thanks,

Possibilities
0 Girls
1 Girl
2 Girls

In each case respectively we have,
$_{10}C_4 \cdot _{12}C_0=210$
$_{10}C_3 \cdot _{12}C_1=1440$
$_{10}C_2 \cdot _{12}C_2=2970$
In total,
4260