Answer: There are 10428 committees that contain at least one member of each class.
Step-by-step explanation:
Since we have given that
Number of freshman = 3
Number of sophomores = 4
Number of juniors = 4
Number of seniors = 5
total = 3 + 4+ 4 + 5 = 16
Number of committees of eight members of the council would contain at least one member of each class is given by
Total - Number of possibility without freshmen - Number of possibility without sophomores - Number of possibility without juniors - Number of possibility without seniors
[tex]=^{16}C_8-^{13}C_8-^{12}C_8-^{12}C_8-^{11}C_8\\\\12870-1287-495-495-165\\\\=10428[/tex]
Hence, there are 10428 committees that contain at least one member of each class.
