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,
Possibilities
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