Question 968562
<pre>
First we find the number of teams of 4 students without regard to gender.

20 students Choose 4 = 20C4 = {{{matrix(1,9,"20*19*18*17"," ","<-four",factors, on,top,starting,with,20)/
matrix(1,16,"","","","","","","4*3*2*1"," ","<-four",factors, on,the,bottom,starting,with,4))}}}{{{""=""}}}{{{4845}}}

Then we find the number of teams with all 4 boys to subtract from that number.

8 boys Choose 4 = 8C4 = {{{matrix(1,9,"8*7*6*5"," ","<-four",factors, on,top,starting,with,8)/
matrix(1,16,"","","","","","","4*3*2*1"," ","<-four",factors, on,the,bottom,starting,with,4))}}}{{{""=""}}}{{{70}}}

And we find the number of teams with all 4 girls to subtract from that number,
too.

12 girls Choose 4 = 12C4 = {{{matrix(1,9,"12*10*9*8"," ","<-four",factors, on,top,starting,with,12)/
matrix(1,16,"","","","","","","4*3*2*1"," ","<-four",factors, on,the,bottom,starting,with,4))}}}{{{""=""}}}{{{495}}}

Answer: 4845 - 70 - 495 = 4280.

Edwin</pre>