We will have the following:
a) The probability that all of the offices are filled by members of the debate team is:
[tex]P=\frac{6}{14}\cdot\frac{5}{13}\cdot\frac{4}{12}\cdot\frac{3}{11}\Rightarrow P=\frac{15}{1001}[/tex][tex]\Rightarrow P=0.01498501499\ldots\Rightarrow P\approx0.015[/tex]b) We will have that the probability that none of the offices are filled with filled by memebers of the debate team is:
[tex]P=\frac{8}{14}\cdot\frac{7}{13}\cdot\frac{6}{12}\cdot\frac{5}{11}\Rightarrow P=\frac{10}{143}[/tex][tex]\Rightarrow P=0.06993006993\ldots\Rightarrow P\approx0.070[/tex]